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Morgan Electro Ceramics forms part of Morgan Technical Ceramics,

a Division of The Morgan Crucible Company plc

www.morganelectroceramics.comwww.morgantechnicalceramics.com

©Copyright November 2007

All Morgan Electro Ceramics manufacturing sites hold ISO 9000 approvals

MorganElectroCeramics

ELECTRO CERAMIC SOLUTIONS

MorganElectroCeramics

PIEZOELECTRIC CERAMICS

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Morgan Electro Ceramics (MEC) has a comprehensive range ofpiezoelectric and dielectric materials from which many products aremanufactured, including transducers, sensors, actuators and high voltage andRF capacitors. MEC has established an enviable reputation for providingvalue-added solutions through world-class research and development,innovative design and, perhaps most important of all, application engineering.

A subsidiary of The Morgan Crucible Company, MEC forms part of the MorganTechnical Ceramics Group. The Group includes Morgan Advanced Ceramicsand from manufacturing locations in North America, Europe and Asia, suppliesan extensive range of products, including ceramic components, braze alloys,ceramic/metal assemblies and engineering coatings.

This brochure contains information about the range of piezoelectric materialsproduced by Morgan Electro Ceramics and gives an introduction to theproperties that may well provide solutions to your design challenges. It doesnot address other materials, many of which are listed below, that are availablefrom the Morgan Technical Ceramics Group of companies, as other literatureexists for these.

For detailed specifications of individual materials, please contact your local areasales person or visit www.morganelectroceramics.com. For more informationon Morgan Advanced Ceramics visit www.morganadvancedceramics.com.

THE MORGAN CRUCIBLE COMPANY PLCThe Morgan Crucible Company plc is the ultimate holding company of agroup of subsidiary engaged in the manufacture and marketing of carbon andceramic components for application in a wide range of industries andservices. It is listed on the London Stock Exchange in the engineering sectorand is part of the FTSE All-Share index. For more information visitwww.morgancrucible.com.

MARKETSMorgan’s electroceramics components, transducers and assemblies areapplied in leading edge technologies such as:

AEROSPACE

AUTOMOTIVE

ELECTRONICS

DEFENCE

MEDICAL

ENERGY

INDUSTRIAL

Morgan continues to develop new materials and value added assembliesto meet the rapidly expanding opportunities in these markets.

MATCHING YOUR REQUIREMENTSTO MORGAN’S CAPABILITIES

APPLICATIONS ENGINEERINGIt is our objective to help our customers as much as possible when designingPiezo components into their products. Applications engineering assistance isprovided as a support facility across the product portfolio.

MATERIALSProcess control of raw materials and their fabrication into ceramiccompounds ensures high quality and repeatability of properties. The controlof the specially formulated ceramic materials are vital to the success of theproduct range and we continually strive to reduce variability in our processes.

TESTING AND CHARACTERISATIONComputer modelling techniques employed in the development of newdesigns requires input of the most accurate material property data available.Morgan focuses on test capabilities to provide this characterisation service totheir customers.

COMPONENTSFirst class manufacturing processes are employed to provide componentsengineered for top performance of electrical and mechanical properties.Quality systems to ISO 9001:2000 are in place to provide the structure forcontrol, function and traceability through the manufacturing facilities.

ELECTRODESExpertise has been developed in the deposition of many electrode materialtypes on to ceramics with patterns, wrap-around and feed throughconfigurations to custom designs. The ability to provide special electrodes canfacilitate the manufacture of the devices into which the ceramic componentsare mounted.

ASSEMBLIES, BIMORPHS AND TRANSDUCERSOur customers have found that there are great advantages in working closelywith us so that we can provide them with a full or sub-assembly. Thetransducers we manufacture to our own design are a complete, fully testedassembly ready for immediate fit into a system.

MULTILAYER TECHNOLOGYPiezo Ceramic Multilayer Actuators (PCMA) operate at reduced drive voltageto deliver small accurate displacements rapidly and with low powerconsumption. This gives advantages over electromagnetic actuators in specificapplications.

QUALITYQuality assurance is an intrinsic part of everything we do from the momentwe receive your initial enquiry to final delivery and after-care. Our totalquality ethos is implemented through an intensive Six Sigma continuousimprovement programme.

All Morgan Advanced Ceramics sites around the world have ISO 9000accreditation. In addition, individual sites hold a variety of industry-specificquality standards.

1

INTRODUCTION

Introduction

Table of Contents

The Nature of Piezoelectric Ceramics

PZT Manufacturing Process

Piezoelectric Applications

Piezoelectric Ceramic Materials

Piezoelectric Property Symbols and Notation

Typical Symbols Employed in Describing Properties of Piezoelectric Materials

Modes of Vibration, Displacement and Voltage

Typical Temperature Properties for PZT Compositions

Dynamic Behaviour of Piezoelectric Ceramics

Useful Electromechanical Relationships

Piezoelectric Sensor

Acoustic Impedance Matching

Shapes and Mechanical Tolerances

Electrodes

Transducers and Sensors

PZT Flexure Elements: Bimorph

Multilayer Actuators

Table of Properties

Navy I Type Piezoelectric Ceramics

Navy II Type Piezoelectric Ceramics

Navy III Type Piezoelectric Ceramics

Navy V Type Piezoelectric Ceramics

Navy VI Type Piezoelectric Ceramics

Custom Piezoelectric Ceramics

Custom Piezoelectric Ceramics

Custom Piezoelectric Ceramics

Single Crystal Materials

Material Cross Reference Table

Glossary of Terms

Samples Ordering Data Checklist

Technical Publications

TABLE OF CONTENT NATURE OF PIEZOELECTRIC CERAMICS

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PIEZOELECTRICITYPiezoelectricity is a property exhibited by certain classes of crystalline materials.When mechanical pressure is applied to one of these materials, the crystallinestructure produces a voltage proportional to the pressure. Conversely, whenan electric field is applied to one of these materials, the crystalline structurechanges shape, producing dimensional changes in the material. These materialsare used as electromechanical transducers.

Piezoelectric properties occur naturally in some crystalline materials and canbe induced in other polycrystalline materials. Pierre and Jacques Curiediscovered piezoelectricity in the 1880’s.

PIEZOELECTRIC CERAMICSQuartz is a good example of a piezoelectric material. Ferroelectric crystals,e.g. tourmaline and Rochelle salt, also exhibit piezoelectricity. In addition to thecrystals mentioned above, an important group of piezoelectric materials arethe piezoelectric ceramics, of which PZT is an example. These arepolycrystalline ferroelectric materials with the perovskite crystal structure, atetragonal/rhombohedral structure very close to cubic. They have the generalformula ABO3, (see Figure 1) in which A denotes a large divalent metal ionsuch as Pb, and B denotes a small tetravalent metal ion such as Zr or Ti.

The PZT ceramics in this data handbook are solid solutions of Lead Titanate(PbTiO3), and Lead Zirconate (PbZrO3), modified by additives, a group ofpiezoceramics generally known as PZT.

The PZT can be fashioned into components of almost any shape and size. Aswell as being strongly piezoelectric, PZT is hard, strong, chemically inert andcompletely unaffected by humid environments.

PIEZOELECTRIC ACTIONSIn a ferroelectric crystal, each cell of the crystal lattice spontaneously polarisesalong one of a series of allowed directions. This spontaneous polarisationdisappears at a critical temperature (the Curie point), above which the crystalbecomes paraelectric.

If the crystal is cooled through the Curie point in the presence of an externalelectric field, the dipoles tend to align in the allowed direction most nearlyaligned with the field. If this crystal is then stressed, the lattice will distort, leadingto a charge in the dipole moment of the crystal (piezoelectric effect). Within acertain stress range (which depends on the crystal concerned), this change in thedipole moment with stress is approximately linear and reversible.

A PZT ceramic may be regarded as a mass of minute crystallites randomlyoriented. After it has been sintered, the ceramic material will be isotropic and willexhibit no piezoelectric effect because of this random orientation. The ceramiccan be made piezoelectric in any chosen direction by a poling treatment, whichinvolves exposing it to a strong electric field. When a field is removed, the dipolesremain locked in alignment, giving the ceramic material a remnant polarisationand permanent deformation (i.e. making it anisotropic), as well as making itpermanently piezoelectric. This poling treatment is usually the final stage of PZTcomponent manufacture.

A PZT component will usually have metal electrodes deposited on its surfaceperpendicular to its poling axis (see Figure 2). When a voltage is applied betweenthem, the body distorts along its poling axis. The random orientation of thecrystallites, and the fact that only certain polarisation directions are allowed,means that it is not possible to get perfect dipole alignment within the field.A reasonable degree of alignment is, however, possible since there are severalallowed directions within each crystal.

Figure 3 illustrates the piezoelectric effect in a cylinder of PZT material. For clarity,the magnitude of the effect has been exaggerated. Figure 3a shows the cylinderunder no-load conditions. If an external force produces compressive or tensile strainin the material, the resulting change in dipole moment causes a voltage to appearbetween the electrodes. If the cylinder is compressed, the voltage will have thesame polarity as the poling voltage (see Figure 3b). If it is stretched, the voltageacross the electrodes will have opposite polarity to the poling voltage (see Figure3c). These are examples of generator action, the conversion of mechanical energyinto electrical energy. Examples of Piezoelectric-induced generator action can befound in cigarette and gas lighters, accelerometers, hydrophones andmicrophones.

If a voltage of opposite polarity to the poling voltage is applied to theelectrodes, the cylinder will shorten (see Figure 3d). If the applied voltage hasthe same polarity as the poling voltage, the cylinder will lengthen (see Figure3e). Finally, if an alternating voltage is applied to the electrodes, the cylinderwill expand and contract at the same frequency as that of the applied voltage(see Figure 3f). These are examples of motor or actuator action, conversionof electrical energy into mechanical energy.

PZT-induced motor action is found in transducers for ultrasonic cleaningequipment, ultrasonic atomisers, fuel injection systems and piezoelectric motors.

Figure 2: Electric dipoles in piezoelectric materials

Figure 1: The Piezoelectric crystal structure.

After poling, the material has a remnant polarisation (Pr) and a remnant stress(Sr) as shown in Figure 4.

AGEING RATES AND TIME STABILITYMost of the properties of piezoelectric ceramics change gradually with time.The changes tend to be logarithmic with time after poling. The ageing rate ofvarious properties depends on the ceramic composition, the geometry and onthe way the ceramic is processed during manufacture. Because of ageing exactvalues of various properties such as dielectric constant, coupling, andpiezoelectric constants may only be specified for a standard time after poling.The longer the time period after poling, the more stable the material becomes.

Exposing the ceramic to one or more combination of the following conditionscan accelerate the ageing process in any ceramic:• High mechanical stress.• Strong electric de-poling field.• High temperatures approaching the Curie point.

Material selection should be based on the conditions of a given application.Typical ageing rates of various material properties can be found on pages30-37 of this handbook.

TEMPERATURE LIMITATIONSAs the operating temperature increases, piezoelectric performance of amaterial decreases, until complete and permanent depolarisation occurs at thematerialís Curie temperature. The Curie point is the absolute maximumexposure temperature for any piezoelectric ceramic. Each ceramic has its ownCurie point. When the ceramic element is heated above the Curie point, allpiezoelectric properties are lost. In practice, the operating temperature mustbe substantially below the Curie point. As a general rule it is not recommendedto exceed half of the materialís Curie temperature in degrees Centigrade. Thematerialís temperature limitation decreases with greater continuous operationor exposure. At elevated temperatures, the ageing process accelerates, and themaximum safe stress level is reduced.

VOLTAGE LIMITATIONSA piezoelectric ceramic can be depolarised by a strong electric field withpolarity opposite to the original poling voltage. The limit on the field strengthis dependant on the type of material, the duration of the application, and theoperating temperature. The typical operating limit is between 500V/mm forsoft piezoelectric materials and 1000V/mm for hard piezoelectric materialsduring continuous application. In bimorph actuators it is possible to apply anelectrical field up to 1.25kV/mm for a soft piezoelectric material. It should benoted that alternating fields can have the same effect during the half cycle,which is opposite to the poling direction.

MECHANICAL STRESS LIMITATIONSHigh mechanical stress can depolarise a piezoelectric ceramic. The limit forthe applied stress is dependent on the type of ceramic material, and durationof the applied stress. For dynamic stress (impact ignition) the limit is lesssevere; materials with higher energy output (high g constant) can be used.For impact applications, the material behaves quasi-statically (non-linear) forpulse durations of a few milliseconds or more. When the pulse durationapproaches a microsecond, the piezoelectric effect becomes linear, due tothe short application time compared to the relaxation time of the domains.

MEC manufactures electro-ceramics materials in a batch process that involves the following basic process stages (see figure 5 below):

NATURE OF PIEZOELECTRIC CERAMICS PZT MANUFACTURING PROCESS

4 5

EQUATION FOR AGEING RATETo predict value X at T days after poling:

XT = Xt+ Xt .AR. (logT - log t)

Where: XT is value of interest at T days after poling.Xt is value at poling date.AR is the Ageing Rate (Positive or Negative)

Figure 3: The Piezoelectric effect on a cylindrical body of piezoelectric ceramics.For the sake of clarity, only one dipole is shown.

Figure 4: Typical hysteresis loop and associated lateral strain or contraction. Figure 5: Typical piezoelectric ceramic manufacturing process

TiO2PbO DopantsZrO2

Weigh Out Raw Material

Milling

Calcine Firing

Milling

Spray Drying

Forming

Binder Burnout

Sintering

Machining

Electroding

Electrode Firing

Poling

Final Test / Inspection

<1000oC

Dry press, isostatic press, Tape cast

<800oC

<1200oC

Silver, Nickel, Gold

MATERIALSSeveral types of piezoelectric ceramic materials are available. Each type istailored towards the requirements of particular applications. This is achieved bychanging the chemical composition of the ceramic to enhance specificproperties. The ceramic materials are arranged in three groups. Hard Materials,Soft Materials and Custom Materials.

HIGH POWER “HARD” MATERIALSHigh power or “hard” ceramics can withstand high levels of electrical excitationand mechanical stress. These materials are suited for high voltage or high powergenerators and transducers.

PZT400 SERIES (NAVY TYPE I)This material is ideally suited for ultrasonic cleaning, sonar, and other high poweracoustic radiation applications. PZT400 Series is a Lead Zirconate Titanate materialcapable of producing large mechanical drive amplitudes while maintaining lowmechanical and dielectric losses. In addition, it can be used under both constantand repetitive conditions. See page 30 for more specific material properties.

PZT800 SERIES (NAVY TYPE III)This material is used in high power applications; even though its piezoelectricactivity level is slightly lower than PZT400 Series. With an extremely low lossfactor, PZT800 Series has the ultimate power handling capability. See page 32 formore specific material properties.

HIGH SENSITIVITY “SOFT” MATERIALSHigh sensitivity or “soft” ceramics feature high sensitivity and permittivity, but underhigh drive conditions are susceptible to self-heating beyond their operatingtemperature range. These materials are used in various sensors, low-power motor-type transducers, receivers, and low-power generators.

PZT5A SERIES (NAVY TYPE II)This material is used as the receiver or generator element in hydrophones,accelerometers, and vibration sensors. PZT5A Series is a Lead Zirconate Titanatewith a high sensitivity, permittivity, and time stability. See page 31 for more specificmaterial properties.

PZT5J1 (NAVY TYPE V)This material is used in fuses, hydrophones, and other applications that require acombination of high energy and high voltage output. PZT5J1 is a Lead ZirconateTitanate with a high permittivity and a high piezoelectric voltage constant. Seepage 33 for more specific material properties.

PZT5H SERIES (NAVY TYPE VI)This material is used in sensitive receivers and applications requiring fine movementcontrol. It has been used in a wide range of applications from hydrophones to inkjet printers. PZT5H Series provides extremely high permittivity, coupling, andpiezoelectric constant. It has the lowest Curie temperature of the “soft” materials(or PZT500 Series family), which restricts its operating temperature range. It haslower time stability. See page 33 for more specific material properties.

CUSTOM MATERIALSMorgan ElectroCeramicsmanufacture a number ofmaterials that do not fall within theDepartment ofDefence (DOD) standards that are often used to define PZTmaterials.

PZT501 – PZT506 (SOFT)These materials are all “soft” and fall between DOD Categories II and V. They rangein Curie temperatures from 270°C to 350°C. All the materials have similar dielectricconstants, but have been optimised for charge constants or coupling coefficients forspecific applications. PZT502 is used as an alternative to PZT5A Series when highersensitivity is required. PZT502 has high acoustic sensitivity, and high coupling, whilemaintaining a high permittivity. See page 34 for more specific material properties.

PZT507 (SOFT)This material is an improved PZT5H Series, developed specifically for bimorphapplications. See page 34 for more specific material properties.

PZT601 (HARD)This material was designed for transducer applications requiring reduced dielectricconstant, high Qm, low dielectric losses and improved electromechanical couplingcoefficients. See page 35 for more specific material properties.

PZT508 (SOFT)This material has been developed to surpass the electrical performance of PZT5HSeries materials while improving the temperatures characteristics by raising theCurie temperature to 220°C. See page 34 for more specific material properties.

PZT5K SERIES (SOFT)This material outperforms PZT5H Series and PZT508 while at the expense ofCurie temperature. This material has very high “d” coefficients and permittivity.See page 36 for more specific material properties.

PZT700 SERIES (SOFT)These materials have been developed for a number of property optimisations. Thematerials have a combination of property stability, good sensitivity and have found usein a variety of sensor applications. See page 35 for more specific material properties.

PZT407 (HARD)This material was developed for its specific combination of permittivity, loss and “d”coefficient. The material in many aspects is similar to materials PZT400 Series, but fallsoutside the Navy I classification. See page 35 for more specific material properties.

PT1This material is a Lead Titanate. Unlike PZT it has low radial mode couplingcoefficients, which therefore provides excellent hydrostatic properties and has thehighest (figure of merit) for any Morgan Electro Ceramic materials. See page 35for more specific material properties.

PMN-PT28/30This new single crystal piezoelectric material has been designed for use in transducerand actuator devices. It has been formulated to exhibit very large electromechanicalcoupling coefficients and also offers high dielectric constants and low dielectric losses.See page 37 for more specific material properties.

Typical Dielectric and Piezoelectric Properties:• Applications include high power sonar projectors, medical imaging, and actuators.• The increased coupling and displacement results in improved bandwidth, sensitivityand source level in applications.

PIEZOELECTRIC APPLICATIONS PIEZOELECTRONIC CERAMIC MATERIALS

6 7

Table 1: Classification of PZT materials by typical applications.

TYPICAL APPLICATIONS SUITABLE MATERIAL PZT TYPE

Ultrasonic CleaningTransducers Hard MaterialSonar Transducers PZT400 Series High Qm

Medical Therapy PZT800 Series High TcUltrasonic welding Low tan�

Cosmetics

SensorsMaterial testing Soft MaterialMedical Diagnostics PZT5A SeriesActuators PZT5J1 Low Qm ( 80)Low power generators PZT5H Series d33>400 pC/NReceivers PZT501 - PZT508Hydrophones PZT5K1Gyroscopes PZT700 SeriesAccelerometers PZT5RInk jet printersBimorphs

UNDERWATER PIEZOELECTRIC APPLICATIONS

AUTOMOTIVE PIEZOELECTRIC APPLICATIONS

CERAMIC PROPERTY DEFINITIONSThe piezoelectric properties are described by a system of symbols and notations.Some of the piezoelectric property symbols are listed and defined in table 2.These symbols identify the property: compliance, electromechanical coupling,etc… The table includes the MKS units used in measuring each property.

Table 2: Ceramic Property Definitions

DIRECTION DEPENDENCEPoled piezoelectric ceramics are anisotropicand the direction of polarisation may be freelychosen, a method of identifying the axes of acomponent is necessary in order to specify itsparameters. The direction of polarisation isconveniently taken as axis 3, with axes 1 and2 perpendicular to this. The terms 4, 5 and 6apply to shear strains associated with the 1, 2and 3 directions (see figure 6 left).

PIEZOELECTRIC EQUATIONSTo a good approximation, the interaction between the electrical and mechanicalbehaviour of the piezoelectric medium can be described by the followingrelationships:

Figure 7 below depicts the phenomenology arising from the mutual couplingsamong the electric, elastic, and thermal fields. The outer quantities are thethermodynamic intensive variables (generalised forces); the inner quantitiesare the extensive variables (generalised displacements).

Strictly speaking, these symbols are used to identify properties of materials only, and should not be used to describe characteristics of actual physical elementsmade of these materials. However, for convenience, some liberties have been taken in the explanations – electric boundary conditions are identified by indicatinglocations and connections of electrodes.

PIEZOELECTRIC PROPERTY SYMBOLS AND NOTATION TYPICAL SYMBOLS EMPLOYED IN DESCRIBING PROPERTIES OF PIEZOELECTRIC MATERIALS

8 9

PROPERTY DEFINITION MKS UNITS

Electromechanical mechanical energy storedCoupling Coefficient electrical energy supplied -

ork electrical energy stored -

mechanical energy supplied

Piezoelectric Strain developedConstants applied stress Metre/Volt

or ord short circuit change density Coulombs/Newton

applied stress

open circuit fieldapplied stress Volt/Newton

g or orstrain developed Metre/Coulombs

applied charge density

Relative DielectricConstant permittivity of material

permittivity of space -K

Modulus of Elasticitystress Newton/Metre²

Y strain

Densitymass Kg/Metre²

� volume

Frequency ConstantControlling Dimension Hz.Metre

N x Resonant Frequency

Figure 6: Notation of axes

WHERE:E = field (V .m

-1)

T = Stress (N .m-2)

S = Strain (SI)D = Dielectric displacment (C .m

-2)

�r = relative permittivity or dielectric constant�0= permittivity of free space (8.85x10

-12F .m

-1)

�T= permittivity under constant stress

Figure 7: Couplings between electrical, mechanical, and thermal fields

SHAPE AXES POLARISATION APPLIED FIELD MODE OF VIBRATIONDIRECTION VOLTAGE OUTPUT DISPLACEMENT APPLIED STRESS

THIN DISC

PLATE

RING

TUBE

ROD

HEMISPHERE

SHEAR PLATES

MODES OF VIBRATION, DISPLACEMENT & VOLTAGE MODES OF VIBRATION, DISPLACEMENT & VOLTAGE

10 11

NOTES: 1 - Equations valid for: (A) plate, disc, ring & shear plate where r, L and W>>thk2 - All variables are metric; use MKS units3 - Constants g31 and g33 and negative values which result in negative strain (contraction) and negative voltage (contraction)4 - Each type of material has particular voltage, stress and temperature limitations.

FREQUENCY CAPACITANCE DISPLACEMENT (STATIC) VOLTAGE (STATIC)

ELECTRICAL EQUIVALENTThe electrical equivalent (see Figure 8) provides the link between the physicalproperty of the crystal and the area of application, the oscillator.

The physical constants of the crystal determine the equivalent values of R1, C1, L1,andC0. R1 is a result of bulk losses,C1, is themotional capacitance, L1 is determinedby the mass, and C0 is made up of the electrodes, the holder and the leads. Whenoperated far off resonance, the structure is simply a capacitor C0 but at the preciseresonant frequency the circuit becomes a capacitor and resistor in parallel. Thereactance of the PZT approaches zero at the point of series resonance and reachesa maximum at the anti-resonant frequency fa (see Figure 9).

An area typically chosen for operation of the oscillator is either near seriesresonance or at the more inductive area of parallel resonance.

At the series resonance (1) the frequency is expressed in equation 6.

Between points A and B, only R1 is remaining, which means the circuit is purelyresistive. At the parallel resonance (2) the frequency is expressed in equation 7.

The impedance between points A and B is at its maximum and is expressedin equation 8.

The measurements of fr and fa give the ratio expressed in equation 9.

Hence equation 10 follows:

The resonant frequency fr can be measured with either of the following twocircuits:

MEASURING METHOD USING CONSTANT VOLTAGE CIRCUITThe fr measuring circuit using a constant voltage source is shown in Figure 10.The oscillator and input resistors R1 and R2 are used to apply a constant voltagesignal to the piezoelectric ceramic transducer. The current passing through thetransducer is measured across output resistor R2. If the transducer's impedanceis much greater than R2, the voltmeter reading is proportional to the transducer'sadmittance. The frequency where the voltmeter reading is maximized is theresonant frequency fr and the frequency where the reading is minimized is theanti-resonant frequency fa. Potentiometer P1 is used to determine the resonantresistance Zr , which is needed to calculate the mechanical quality factor Qm.

TESTING OF PZT COMPONENTSBelow is a list of the various electrical parameters which are normally measuredto qualify PZT components. In the absence of a customer specification, MorganElectro Ceramics will apply internal limits.

• Capacitance• tan�

• Coupling (Kp, Keff)• Fr, Fa• Zr, Za• Insulation Resistance• Other parameters as per customer request.

TYPICAL TEMPERATURE PROPERTIES FOR PZT COMPOSITIONS DYNAMIC BEHAVIOUR OF PIEZOELECTRIC CERAMICS

12 13

NOTE: ABOVE CURVES ARE REPRESENTATIVE DATA ONLY.

Figure 8: The electrical equivalent circuit for a PZT resonator.

Figure 9: The reactance of the PZT resonator varies with frequency of operationnear resonance.

Figure 10: Resonant frequency method using constant voltage.

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Temperature (oC) Temperature (oC)

Temperature (oC) Temperature (oC)

MEASURING METHOD USING CONSTANTCURRENT CIRCUITThe fr measuring circuit using a constant current source is shown in Figure 11.Resistor R3 regulates the current passing through the piezoelectric ceramictransducer. If R3 is much greater than the transducer's impedance, the voltmeterreading is proportional to the transducer's impedance. The frequency where thevoltmeter reading is minimized is the resonant frequency fr, and the frequencywhere the reading is maximized is the anti-resonant frequency fa.

CIRCUIT CONSIDERATIONSNON-RESONANT MECHANICALLY DRIVEN DEVICESFor most practical design purposes, a non-resonant piezoelectric generatordevice, such as a microphone or accelerometer, together with the load onthe device, may be represented by the equivalent circuit of figure 12a, whereCe represents the capacitance of the piezoelectric element, Rc is the shuntleakage resistance of the device, CL is the shunt load capacitance, representsthe load resistance and eL represents the load potential.

The values of the shunt leakage resistance and the capacitance of thepiezoelectric element are dependent on the dimensions of the element and,in the case of leakage resistance, also upon the dryness of the surface.

Under normal operating conditions, the value of this resistance is many timesgreater than the normal load resistance, ranging from several hundredmegohmsto many thousands of megohms. Generally, except at very low frequencies, thecapacitances in the circuit have reactances very much lower than the circuitresistances. Under these conditions, the circuit reduces to the simple capacitivevoltage divider circuit (see Figure 12b).

It can be seen from this circuit that the shunt load capacitance CL of wiring, cable,and amplifier input does not bring about a relative loss of high frequency responseas in the case of resistive or inductive sources shunted by capacitance loads, butinstead reduces the output at all frequencies (except very low frequencies asdiscussed in the next paragraph). By the application of elementary network theory,the basic circuit can be reduced to the equivalent circuit of figure 12c, which isuseful for analysing the low frequency response. From this it can be seen that whenthe combined reactance of the piezoelectric and circuit capacitances in parallelapproaches the combined resistance, the low frequency response begins to fall off.This is analogous to the situation existing in conventional RC-coupled amplifiers.

NON-RESONANT ELECTRICALLY DRIVEN DEVICESIn the case of non-resonant piezoelectric devices, which are electrically driven,the electrical impedance of the device may, for most practical purposes, beconsidered to be purely capacitive. For all frequencies well below the firstmechanical resonance of the device, the electromechanical relationships aresuch that the displacement of the piezoelectric element from its normal position,at any instant, is directly proportional to the electric charge applied at that instant.

RESONANT DEVICESThe electrical impedance of a piezoelectric device is, in reality, more complicatedthan the simple capacitor representation generally employed in discussing non-resonant devices. A more accurate representation would be a capacitorrepresenting the static capacitance of the piezoelectric element, shunted by animpedance representing the mechanical vibrating system. In most non-resonantdevices, the latter impedance may be approximated by a capacitor. Therefore,we have a capacitor in parallel with a capacitor, hence the single capacitorrepresentation.

In devices designed for operation at resonance, the impedance representingthe mechanical system may become, at resonance, a resistance of relativelylow value and this is shunted by the same static capacitance.

The shunt static capacitance generally is undesirable, whether the device isdesigned for operation at resonance or for broadband, below resonanceoperation. In electrically driven devices, it shunts the driving amplifier or othersignal source requiring that the source be capable of supplying extra current.In the case of mechanically driven devices, the static capacitance acts as a loadon the active part of the transducer, reducing the electric output.

In non-resonant devices, not much can be done about the shunt capacitance,except choose a piezoelectric material having maximum activity. In resonantdevices, however, the static capacitance may be “neutralised” or matched byemploying a shunt or series inductor chosen to resonate with the staticcapacitance at the operating frequency. This is illustrated in Figure 13.

POWER LIMITATIONSThe acoustic power handling capacity of a radiating transducer is limited bythe following factors:1. Dynamic mechanical strength of the ceramic2. Reduction in efficiency due to dielectric losses3. Reduction in efficiency due to mechanical losses4. Depolarisation of the ceramic due to electric field5. Depolarisation of the ceramic due to temperature rise6. Instability resulting from the positive feedback between dielectric losses

and internal heating (factor 2 and 5)

In practice, power limitations are imposed by factors 2 and 5 and the feedbackbetween them (factor 6), depending on the composition of the ceramic. Factors1, 3 and 4 may be neglected. Factor 1 may be reduced through mechanical biasin sonar, ultrasonic, and other similar applications. Factor 3 may be generallydisregarded, since mechanical losses are negligible compared to dielectric losses.

In the case of factor 4, the electric field necessary to cause sufficient depolarisationwill create extremely undesirable operating conditions with very high dielectriclosses, resulting in low efficiency.

A transducer may be efficiency-limited, temperature-limited, or dynamic-strengthlimited. Dynamic strength is significant only when a transducer is not mechanicallybiased and the ceramic has a high mechanical quality factor Q . A low frequency,low duty transducer is efficiency-limited. A high frequency continuous dutytransducer is temperature-limited. Temperature limited transducers aredependent on the efficiency of the heat removal from the ceramic. Betweenthese two extremes, the specific limitation is dependent on the mechanical designof the transducer. An absolute value on the power limitation of the ceramiccannot be determined without knowledge of its operating conditions.

The equations pertaining to the power handling capacities of the materialmay be readily derived from lumped equivalent circuits. It can be shown thatthe acoustic power density P per cubic metre is given by equation 11.

It is assumed that the mechanical losses in the ceramic and the housing arenegligible compared to dielectric losses. This tends to hold for materials withQ > 100. The power per cubic meter dissipated in the ceramic by dielectricdissipation Pd is given by equation 12.

The efficiency of the transducer � considering only the internal losses of thematerial is approximated by equation 13.

With high values of Q power handling capacity of the material is limited attimes by the dynamic tensile strength, even though a bias compressive stressas high as 80MPa is used with PZT-400 series. In this case, the acousticpower is given by equation 14.

These equations may be simplified for the specific case of a matchedtransducer. Matching is the term applied to the process of adjusting theacoustic load so that it corresponds to the image impedance of thetransducer, which is treated as a bandpass filter. In this case, an inductor equalto (see equation 15) is connected across the transducer.

The impedance of the driving electric generator is set equal to the imageimpedance in order to maximise the transducer bandwidth, where thegenerator resistance, RG and the mechanical load impedance, RT, are givenin equation 16; the bandwidth is given by equation 17; and the acousticpower and efficiency are given by equation 18.

Table 3 lists the relative power for PZT-400 and PZT-5A series at resonancefor the same acoustic load for a given volume of material, assuming that thematerial is limited by the dielectric losses tan �=0.04

DYNAMIC BEHAVIOUR OF PIEZOELECTRIC CERAMICS DYNAMIC BEHAVIOUR OF PIEZOELECTRIC CERAMICS

14 15

Table 3: Relative power for PZT-400 and PZT-5A series.

MATERIAL MODE TEMPERATURE (ºC) RELATIVE POWER

PZT-400 series Parallel 25 100PZT-400 series Parallel 100 65PZT-400 series Transverse 25 23PZT-400 series Transverse 100 12.5

PZT-5A series Parallel 25 2.7PZT-5A series Parallel 100 3.2PZT-5A series Transverse 25 0.5PZT-5A series Transverse 100 0.6

Figure 11: Resonant frequency method using constant current.

Figure 12: Non-Resonant Mechanically Driven Device

Figure 13: Resonant PZT device matched by inductor.

m

m

m

The mechanical losses can be determined from the mechanical quality ordamping factor, Qm, from equation 32.

Qm can also be determined approximately from the frequency responsecurve as follows.

The frequency difference f2 - f1 is the frequency bandwidth at about 3dB wherethe amplitude is 1/ 2 of its maximum value. Of these losses, the dielectriclosses are usually the most significant. Therefore, it is recommended thatmaterials with a low dissipation factor be used for high power applications,particularly since these losses increase with power. For high intensitytransducers, the overall electro-acoustical efficiency � is given approximately byequation 33.

It should be noted that at high drive levels QE and Qm are not constants. They areusually lower than the low drive level values. The dielectric permittivity of thematerial, and therefore the dielectric constant and capacitance, decreases as theapplied frequency (mechanical or electrical) exceeds each resonant frequency of theparticular ceramic part. For static operation, well below the first resonancefrequency, the dielectric permittivity is r 33 (free). For dynamic operationwell aboveall resonance frequencies of the ceramic part, the material behaves as if it wasclamped (strain= 0), and the electric permittivity is r 33 (clamped). Between each,the permittivity is the product of the static permittivity and a loss term based on thecoupling of the resonance mode each resonance point the applied frequency hasexceeded, as described in equation 34 (above first resonance), equation 35 (abovesecond resonance), and equation 36 (above third resonance).

Where k1, k2, and k3 represent the coupling factors for the particular resonance.For a thin plate, k1 and k2 are k31 and k’31 (length and width respectively), and k3

is kt (thickness).

For a thin disc, k1 is kp (radial), k2 is kt (thickness), and there is no thirdresonance. For a rod, k1 is k33 (length), k2 is k’p and there is no third resonance.In addition to fr and fa (series and parallel resonance frequencies), there is afrequency fm, at which the transducer’s electromechanical transduction ismaximised. This frequency represents the maximum sensitivity for receivers orthe maximum output for drivers. This frequency, the bandwidth, and theoutput are all dependent on the external resistive load, Rext. When k<<1, fmmay be calculated using equation 37.

The maximum bandwidth, B, obtainable by electrical tuning, is approximatelyequal to the product of the coupling coefficient and the series or parallelresonance frequency as described in equation 38.

If the mechanical quality factor is high (Qm>Q), the external resistance Rext

for a fairly flat frequency response can be approximated by equation 39 forparallel inductance, or equation 40 for series inductance.

USEFUL ELECTROMECHANICAL RELATIONSHIPS

STATIC AND QUASI-STATIC OPERATIONUnder static or quasi-static (below resonance) conditions, the magnitude of thepiezoelectric effect is given by piezoelectric “d” and “g” constants. For the caseof the direct piezoelectric effect where the material develops an electric chargefrom an applied stress, the definitions for “d” for constant field and “g” forconstant dielectric displacement should be used. For the converse effect wherethe material develops a strain from an applied electric field, the definitions for“d” and “g” for constant stress should be used. These “d” and “g” coefficientsare related by equation 19 for plates and discs, and equation 20 for rods.

The permittivity of the material is related to both the permittivity of free spaceand the dielectric constant of the material according to equation 21.

At frequencies far below the mechanical resonance frequency, the electro-mechanical coupling factor, k, can be calculated by equation 22 for plates,equation 23 for discs, equation 24 for rods, and equation 25 for shear plates.

The coupling factor is a useful expression relating the amount of energy thatcan be changed from the electrical form to the mechanical form, or vice versa,for the different operational modes. The coupling factor can be expressed asequation 26.

This value, although related, should not be considered the overall efficiency ofthe electromechanical transduction, since it does not take into account electricaland mechanical dissipation or losses. When a transducer is not operating atresonance or if it is not properly tuned and matched, the efficiency can be quitelow. A properly designed transducer can operate at well over 90% efficiency.

The pressure P, which a ceramic driver can impart, is given approximately byequation 27.

DYNAMIC OPERATIONUnder dynamic conditions, the behaviour of the piezoelectric material is muchmore complex. It can be characterised in terms of an equivalent electrical circuit,which exhibits the conditions of parallel and series resonance frequencies. Toapproximate these frequencies, measure the frequency of the minimumimpedance (fr) and maximum impedance (fa) for the component, since theydiffer by a very small amount (<0.1%). The coupling coefficient, K, can bederived from these frequencies. This derivation is somewhat complex as K isdependent on both the shape of the component and the mode of vibration. Themost useful of these relationships are described in equation 28 for plates,equation 29 for discs, and equation 30 for rods.

In addition to the coupling coefficient, the total efficiency of a transducerdepends on the mechanical and dielectric losses.

The dielectric losses, tan �, are given by the dissipation factor, D.F., as describedin equation 31.

USEFUL ELECTROMECHANICAL RELATIONSHIPS

16 17

Where k33 is the relative dielectric constant of the material and 0 is thepermittivity of free space (8.85x10-12 F/m).

(Discs and plates)

(Rods)

(Rods)

(Plates)

(Discs)

(Rods)

(Plates)

(Discs)

Where d is equal to d33 for thickness mode operation or d31 for radial or transversemode, E is the applied electric field, and Y11 is Young’s Modulus for that material.

Where S is the compliance of the material.

Where QE is the electrical damping.

Where CP is the low frequency capacitance and Zr is the minimum impendance atresonance.

(Above first resonance)

Where QA is the mechanical quality factor due to the acoustical load alone.

(Above second resonance)

(Above third resonance)

(Parallel inductance)

(Series inductance)

T

S

T

E

THE PIEZOELECTRIC SENSORPiezoelectric measuring systems are activeelectrical systems, which can measuremechanical quantities such as force,acceleration or pressure. That is, the crystalsproduce an electrical output only when theyexperience a change in load. For this reason,they cannot perform true staticmeasurements.High impedance transducers such aspiezoelectric sensors, hydrophones, and someaccelerometers require an amplifier, which

converts a transfer of charge into a change of voltage. Because of the high DirectCurrent (DC) output impedance of these devices, appropriate buffers are required.The basic circuit for an inverting charge sensitive amplifier is shown in Figure 14.

Charge-emitting transducers produce an output charge, �Q, and theiroutput capacitance remains constant. This charge would normally producean open-circuit output voltage at the transducer output equal to �Q/C.

However, the voltage across the transducer is held constant by the virtualground of the op amp (R1 is usually small), the charge is transferred to capacitorC2 producing an output voltage expressed in equation 54.

In an actual application, the charge amplifier only responds to AC inputs. Theupper and lower cutoff frequencies are given in equation 55.

TYPICAL FREQUENCY RESPONSETwo of the more important considerations in the practical use of charge amplifiersare time constant and drift. The product of the feedback capacitor C2 and thefeedback resistor R2 determines the time constant (�) of a charge amplifier, definedin equation 56.

Drift is defined as an undesirable change in output signal over time, which isnot a function of the measured variable.

The longer the time constant is, the better the low-end frequency response andthe longer the usable measuring time. This is expressed in equation 57 and 58.

Figure 15 below illustrates the typical frequency response of an accelerometer.Below the lower cutoff frequency it is considered as DC mode.

HYDROPHONESInterfacing the outputs of highly capacitivetransducers such as hydrophones, accel-erometers, and condenser microphones tothe outside world presents many designchallenges. Previously, designers had to usecostly hybrid amplifiers consisting of discretelow-noise JFETs in front of conventionaloperational amplifiers to achieve the lowlevels of voltage and current noise requiredby these applications.

In sonar applications, a piezoceramic cylinder is commonly used as the activeelement in the hydrophone. A typical cylinder has a nominal capacitance ofaround 6,000pF with a series resistance of 10�. The output impedance istypically108� or 100M�.

Since the hydrophone signals of interest are inherently Alternating Current (AC)with wide dynamic range, noise is the overriding concern among sonar systemdesigners. The noise floor of the hydrophone and the hydrophone preamplifiertogether limit the sensitivity of the system and therefore the overall usefulness ofthe hydrophone. Typical hydrophone bandwidths are in the 1kHz to 10kHzrange. The AD743® /AD745®, MAX4252® or LT1792® operationalamplifiers respectively from Analog Devices, Maxim Integrated Products andLinear Technology, with their low noise figures and high input impedance are idealfor use as hydrophone amplifiers. Further reading and application notes can befound on the manufacturers’ web site.

PIEZOELECTRIC SENSORUSEFUL ELECTROMECHANICAL RELATIONSHIPS

18 19

PZT400 PZT5A PZT800SERIES SERIES SERIES

AC depoling field >1.0 0.7 >1.5

AC field for tan � = 0.04 @25°C (a) 0.39 0.45 >1.0

% increase of r 33 at aboveelectric field 17 11 10

AC field for tan � = 0.04 @100°C 0.33 0.045 n/a

Maximum rated static compressive @25° C82.7 20.734.5 (b) 82.7stress (maintained) PARALLEL tothe polar axis @100°C 41.4 20.7 41.4

% change of r 33 with stressincrease to rated maximumcompressive stress at 25°C ~25% (c) ~ -3% (d) ~18% (c)

% change of d33 with stressincrease to rated maximum ~ 0.1% @20.7compressive stress at 25°C (b) ±15% (c) ~ -13% @34.5 6% (c)

Maximum rated compressive stress @25°C 55.2 13.8 55.2(maintained) PERPENDICULAR to @100°C 27.6 13.8 27.6the polar axis

Maximum rated hydrostatic pressure 345 138 345

Compressive strength >517 >517 >517

Tensile strength, static (e) 75.8 75.8 75.8

Tensile strength, dynamic (peak) (e) 24.1 27.6 34.5

Figure 15: Typical frequency response of an accelerometer.

Figure 14: Simplified model of a charge amplifier.

(Rods)

(Rods)

(Rods)

(Plates)

(Plates)

(Plates)

(Hydrostatic charge constant & coefficient)

Many of the calculated parameters before are interrelated. Thus, many usefulrelationships can be derived. A few of the most useful relationships are describedin equations 41 through 53.

HIGH SIGNAL PROPERTIES

(a) The value of tan� at a given electrical field is a function of time after poling or after anymajor disturbance such as exposure to an elevated temperature.

(b) After appropriate stabilising treatment. This consists of a temperature stabilisation plus a fewminutes soak at the appropriate static stress. The temperature stabilisation is, however,more important than the stress soak.

(c) In range to 70MPa(d) In range to 35MPa(e) These figures are dependant upon configuration and perfection of fabrication. The static

tensile strength figures were obtained from bending tests on thin Bimorph structures, whilethe dynamic tensile strength figures were obtained from measurements of high amplituderesonant vibration rings. The latter tests are more sensitive to minor flaws.

Table 4 High signal properties for PZT400, PZT800 and PZT5A series.

In this table units of electrical field are in kV/mm and stress is in MPa.

T

T

In the second procedure, the finite thickness of the piezoelectric element isconsidered. A transmission line model (KLM) is used, and optimum bandwidthand maximum efficiency are imposed to determine both the number of �/4matching layers required and the acoustic impedance of each one.

First, the number of matching layers is determined from Za, Zp, and theeffective piezoelectric coupling coefficient of the ceramic (kt2). Then theimpedance of each layer is determined. Two cases are analysed: For a single�/4 matching layer, acoustic impedance is given as in equation 65.

For a double matching layer it is given by equation 66.

Where Zm1, and Zm2 denote the acoustic impedance of the first and secondmatching layer, respectively.

Acoustic impedance is given by equation 67.

Where � is the density and c the acoustic velocity of the material.Wavelength is expressed in equation 68.

Where � is the wavelength, c is the sound velocity and f the frequency.

Table 5: Materials acoustic characteristics

In general, the stronger influence of the attenuation in the matching layer isobtained for the single matching layer scheme.

EXAMPLEA piezoelectric ceramic element has the following characteristics:• Material: PZT501• Shape: Disc• Diameter: 10mm• Thickness: 1mm

The radial resonant frequency of the piezoelectric transducer is:

In this example, the piezoelectric transducer must be interfaced to salt waterwith a double quarter-wavelength matching layer.

Using equation 64, the acoustic impedance of thematching layers can be calculated.

From table 5, Aluminium 6262-T9 and PVDF seem to be adequate materialsfor the application as their acoustic impedance is close to calculated values.

The wavelength in each material can be calculated from equation 68.

Thus giving matching layer thicknesses of:

ACOUSTIC IMPEDANCE MATCHING

21

Piezoelectric transducers require the use of impedance matching layers topartially mitigate the impedance mismatch between a media through whichultrasonic wave signal is propagated and the piezoelectric element. Severalmatching configurations have been studied, examples are single quarterwavelength (�/4) layers and variations of this configuration such as (�/8) and(n+1).�/4, stacks of �/4 layers, half-wavelength configurations (�/2), and astack of very thin matching layers whose total acoustic thickness is (�/4). Inany of these configurations, a key aspect for the successful design of matchedtransducers is the acoustic impedance of the outer layer.

DESIGN OF QUARTER WAVELENGTH MATCHING LAYERSThe impedance mismatch between a media and piezoelectric ceramics hastwo main consequences for the design of the piezoelectric transducers:•Sensitivity is low•Bandwidth is narrow

A single matching layer can improve sensitivity, but the widening of thefrequency bandwidth requires the use of two or more matching layers.

There are two different procedures to determine the optimum acousticimpedance of the �/4 matching layers. They lead to somewhat different results,and they are briefly reviewed here. The first one is based on the optimization ofthe energy transfer through the two interfaces involved in the problem:Piezoelectric element-Matching layer and Matching layer-Media of propagation(air, water, gas, etc…), in which the piezoelectric element is considered an infinitelayer. At a plane interface between media A and B, having acoustic impedancesZA and ZB, respectively, solution of reflection and transmission problems fornormal incidence is given by equation 59 below and represented in figure 16.

Where u is the particle velocity, and subscripts i, r, and t denotes incident,reflected, and transmitted waves respectively.

The transmitted wave through a matching layer, from a piezoelectric elementto a media, is the sum of the contribution of each of the multiple reverberationswithin the matching layer. At the resonant frequency of a quarter-wavelengthmatching layer, all terms in this summation have the same phase when thewave leaves the matching layer; a geometrical series is obtained. The series thatrepresent the amplitude of the transmitted wave and its summation are givenin equation 60.

Where t represents the ratio of transmitted to incident wave amplitude, andr represents the ratio of reflected to incident wave amplitude. From equation60, they are given as equation 61:

Subscripts 1 and 2 denote the two interfaces involved: Piezoelectric ceramic-Matching layer, and Matching layer-Media of propagation.

Z is the acoustic impedance, and subscripts p, m, and a, denote thepiezoelectric ceramic, the matching layer, and the media of propagationrespectively.

Considering plane waves, the ratio of energy flux transmitted to the media ofpropagation to the energy flux incident on the matching layer (�t) is given inequation 62:

For maximum transmitted energy, given the values of Zp, Za, the value of Zmis given by the simplified equation 63.

The same result is obtained if the multiple reverberations inside the matchinglayer are ignored, and the amount of energy transmitted through each interfaceis maximised. However, considering multiple reverberations is of interest inorder to account for the contribution of the attenuation. For an ideal quarter-wavelength matching layer (no attenuation and acoustic impedance given byequation 63) working at its resonant frequency, there is no energy loss (�t=1);and in equation 63 can be generalised for a stack of “n” matching layers, theimpedance of the j

thlayer is given as in equation 64.

20

ACOUSTIC IMPEDANCE MATCHING

MATERIAL SOUND VELOCITY ACOUSTIC IMPEDANCE[m/s] [106xkg(m2s)] OR [MRay1]

Brass 4430 36.7Inconel 5700 47.2Monel 5400 47.6Aluminium 6262-T9 6380 17.41PVDF 2300 4.2Carbon (soft) 3310 7.31Alumina oxide 10000 32Silver 3600 38Iron (cast) 4600 33.2Salt water 1531 1.569Polyurethane, RP-6400 1500 1.560Neoprene 1600 2.1Hard PVC 2060 2.78Rubber Butyl 1800 2.0Zinc 4200 29.6PZT500 series 4350 33.71PZT5H series 3800 28.5PZT400 series 4600 34.5PZT800 series 4600 35

Figure 16: Transducer with transmission and reflection paths Figure 17: Piezoelectric transducer with matching layers

SOLDERING TO SILVER ELECTRODESSoldering electrical wires to the screen-printed silver electrodes make excellentand time-stable connections. Processes are tightly controlled during manufactureto do everything possible to supply parts with high quality electrodes. Thethickness, solderability and bond strength of electrodes are routinely tested. Thethickness of the screen-printed silver electrode is in the range of 3µm up to 10µm.

Occasionally there can be problems with wetting the solder on the silver surfaceand soldering can then be difficult. This phenomenon is mainly caused by areaction between sulphuric molecules in the atmosphere with the silver surface- with the formation of a silver sulphide layer on the surface of the part. Theformation and thickness of this layer is influenced by several factors such as age,pH, humidity, etc.

In order to overcome such problems, it isgood practice to gently clean the surface ofthe electrodes on the part before soldering.A glass brush (RS 514-868) or steel wool isvery useful for this operation. Figure 18 (left)shows various PZT components with firedon silver electrodes.

When soldering is performed it isimportant that the temperature does not exceed the Curie point of thematerial, since this will immediately depolarize the piezoelectric phase. Fornormal PZT types, use soldering temperatures between 240 and 300°C.Furthermore, silver is soluble in the solder, and if the solder time is too longthe electrode will completely dissolve in the solder. In order to increase thepossible solder time, use a solder with silver content of 2-4%. Even if thepossible soldering time is increased with this type of solder, the solder timemust not exceed 2-4 seconds (see Figure 19).

Mechanical stressing of the joint after completion must be avoided or at worstkept to the minimum. The positioning of the wire when the connection is madeshould be as close as possible to the final position. Bending the wire at rightangles to its original position will almost certainly break the joint due to the highpeeling stress introduced.

It should also be noted that the piezoceramic parts do not only have a highpiezoelectric coefficient, but also a significant pyroelectric coefficient. This meansthat the increase in temperature introduced by the soldering process willgenerate an electrical charge. This charge can be released as a spark, which,even if completely harmless to humans, can be very unpleasant for the operator.

It is therefore be recommended to solder parts in short-circuit conditions.

N.B: If a piezoelectric element is heated to its Curie point, the charges can bedisordered and the element becomes completely depolarised. A safe operatingtemperature would normally be about half way the Curie point.

CONNECTION TO NICKEL ELECTRODESOur Nickel electrodes vary depending upon the deposition method used:

• Chemically plated

• Electroless Nickel

• Evaporated Nickel

For connection, we therefore recommend two different methods:

EVAPORATED NICKELConductive epoxies are typically used to provide a consistent reliable electricalconnection.

ELECTROLESS NICKELMaterials used: 15W soldering iron, Flux (Superior 30 or equivalent),unleaded solder (if possible), glass brush, Q-Tip and Ethanol. Gold sputteredelectrodes are also available.

Procedure: Pre-heat the soldering iron then clean the electrode area using Q-Tip with Ethanol, or a mild abrasive such as an eraser. Melt some solder onthe tip of the soldering iron. Tin the lead with solder and then dip the thinnedlead into the flux. Place lead on the electrode area and place the soldering ironwith mild pressure on the lead until the solder flows onto the electrode. Holdthe lead stationary for approximately 5 seconds to allow solder to solidify.

KEY POINTS TO REMEMBER1. Always keep the tip coated with a thin layer of solder.

2. Use fluxes that are as mild as possible but still provide a strong solder joint.

3. Keep temperature as low as possible while maintaining enough temperatureto quickly solder a joint (2 to 3 seconds maximum for electronic soldering).

4. Match the tips size to the work.

5. Use a tip with the shortest reach possible for maximum efficiency.

6. Too high soldering temperatures and too large temperature gradient such asrapid heating or cooling may cause electrical failures and mechanical damagesof the devices.

ELECTRODES

23

TAPERED STAVE

BARREL STAVE

SHAPES AND MECHANICAL TOLERANCES

22

SHAPESCustom shapes are available as well as the shapes shown tothe left of this page.

Parts can be made to the size ranges shown, but not in everycombination of thickness and lateral dimensions.

A separate list of standard sizes of parts available can be obtainedon request.

STANDARD MECHANICAL TOLERANCESTolerances on machined dimensions apply to most components.For large size parts, confirmation of the tolerances achievable willneed to be agreed prior to placing an order.

Components can be produced to tighter tolerances (e.g.Concentricity within 0.13mm (0.005") TIR and surface finish(Ra) within 1.6�m (62�in)).

Care should be taken not to over-specify a tolerance as thiscan significantly increase costs.

FREQUENCY TOLERANCESBetter than ±5% up to 2MHzTyp. ±7% above 2MHzCloser tolerances are available on request

TYPICAL SIZE RANGEOther sizes outside the range may be possible. Pleasecontact the manufacturing site for more details.

As "Fired" tolerances±0.3mmor±3%whichever is greater

STANDARD MECHANICAL TOLERANCES

Legend:

Electrode

PZT Ceramic

FROM TO

OUTSIDE DIAMETER 1mm (0.04") 150mm (5.9")INNER DIAMETER 0.5mm (0.02") 140mm (5.5")THICKNESS 0.15mm (0.006") 25mm (1")

FROM TO

DIAMETER 1mm (0.04") 254mm (10")THICKNESS 0.08mm (0.003") 25mm (1")

FROM TO

LENGTH 1mm (0.04") 150mm (5.9")WIDTH 1mm (0.04") 150mm (5.9")THICKNESS 0.08mm (0.003") 25mm (1")

FROM TO

OUTSIDE DIAMETER 1mm (0.04") 150mm (5.9")INNER DIAMETER 0.5mm (0.02") 140mm (5.5")LENGTH 1mm (0.04") 150mm (5.9")

FROM TO

OUTSIDE DIAMETER 6mm (0.24") 150mm (5.9")WALL THICKNESS 1mm (0.04") 10mm (0.39")

FROM TO

DIAMETER 6mm (0.24") 150mm (5.9")THICKNESS 1mm (0.04") 10mm (0.39")

Outside Diameter ±0.15mm ±0.006"

Inner Diameter ±0.15mm ±0.006"

Length & Width ±0.15mm ±0.006"

Thickness ±0.05mm ±0.002"

Squareness (edge to face) Within 0.15°

Concentricity 0.2mm TIR 0.980 TIR

Surface Flatness (Lapped Parts) 12µm (0.012mm) 0.0005"

Surface Flatness (Large Sliced Parts) 15µm (0.015mm) 0.0006"

Parallelism (Lapped Parts) 12µm (0.012mm) 0.0005"

Parallelism (Large Sliced Parts) 60µm (0.06mm) 0.002"

Surface Finish (Ra) 3µm (0.003mm) 0.0001"

DISC

PLATE (SQUARE & RECTANGLE)

RING

TUBE

HEMISPHERE

FOCAL BOWL

Figure 19: Soldering profile for most PZTs on silver fired electrodes

Figure 18: Various PZT components

C = Constraint PointSR = Stress Relief Bend

Figure 20: Different configurations for wire bonding to ceramics

Recommended soldering temperature - Time profile for PZTs

TRANSDUCERS & SENSORSMorgan Electro Ceramics is a world leader inthe field of electroceramics and manufactures awide range of specialised piezoelectrictransducers and sensors for mechanical,electrical and electronic applications. With designcentres and manufacturing locations in Europeand the USA, Morgan specialises in designingand manufacturing complete solutions for OEM

applications. Many of our customers find that Morgan’s complete Sensor andTransducer divisions offer a Total Solution to their needs. Main markets servedincluded medical, aerospace, industrial and defence.

PRODUCTS:• Ultrasonic Transducers• Sensors

CAPABILITIES:• Transducer Manufacture

• Transducer Design

• Transducer Testing

ULTRASONIC TRANSDUCERSOur ultrasonic transducers are designed usingMorgan’sworld leading piezomaterials.These materials have extremely good electrical loss properties, high coupling and

excellent mechanical properties, which enables usto design and manufacture some of the mostefficient ultrasound generators available on themarket. In addition to the custom designs, wehave standard designs for the followingapplications.•Ultrasonic Cleaning•Ultrasonic Therapy•Pre-stressed fibre wrapped tubes

APPLICATION & MARKETS

Medical Industrial

Dental Descalers Ultrasonic Cleaning

Ultrasonic scalpel Ultrasonic Welding

Cell disruption Sonochemistry

Ultrasonic phacoemulsion Degassing

DESIGNWe design our transducers using in housemodelling software backed up with extensivetest and measurement capabilities, whichincludes laser vibrometry for displacementmeasurement. Designing a drive circuit to matchtransducer characteristics is critical for goodsystem performance.

Morgan’s transducers are fully tested to ensure consistent electrical andmechanical characteristics to ensure good compatibility with our customer’sdrive circuits.

DESIGN CAPABILITY:

• 3D Finite-Element Analysis software

• Proprietary computer modelling software

• Custom formulated PZT & shapes

• Single / multi-layer products

• Stack transducers

• Flexural mode transducers

• Bonded / encapsulated assemblies

•Bimorph actuators and sensors

ULTRASONIC CLEANINGMorgan’s range of ultrasonic cleaningtransducers uses the latest high performancePZT material and are designed to operate incontinuous mode in harsh environments. Theyhave been proven in service over the lastdecade and are used by many of world’sleading manufacturers of ultrasonic cleaningsystems in applications as diverse as cleaning

semiconductors and engine parts. Standard transducers are available with eitherexposed contact for soldering leads or complete with flying leads. All of Morgan’sstandard transducers are varnish treated to maximise the resistance to humidityand other atmospheric conditions. These transducers have a grit-blasted base toassist with adhesive bonding to tanks. In many types a thread is also provided toenable mounting top tanks with threaded studs. In addition to this, Morgan isable to design and manufacture custom transducers for specific frequencies andpower ratings. This includes the ability to supply transducers for multi frequencyoperation. These designs are made with the help of Morgan’s bespoke designsoftware and extensive testing facilities.

TRANSDUCERS FOR ULTRASONICTHERAPYUsed by physio and beauty therapists aroundthe world, ultrasonic therapy is well proven inthese fields. Morgan designs and manufacturestransducers for massaging, treatment andtherapy of skin and soft tissue. These transducersare generally custom designs with bespokemechanical dimensions, wiring and frequencies

to suit the OEM. Dual frequency transducers (typically 1 and 3 MHz) can also bedesigned. These transducers use Morgan’s high performance low loss PZTmaterials to ensure optimum efficiency and thus minimise self-heating.

PRE-STRESSED FIBRE WRAPPED TUBESFor the Sonar Industry Morgan supplies pre-stressed fibre wrapped PZT tubes. Fibrewrapping enable high energy projectors to bedesigned whilst minimising the risk of ceramicfailure through excess tension. Small tubes (upto 100mm) are usually manufactured using amonolithic PZT ceramic tube. Larger tubes(up to 500mm) are constructed with multiple

tapered PZT ceramic segments. Morgan’s high coupling and low loss materialsare always the basis of a high efficiency tube.

TRANSDUCERS & SENSORS

25

LEAD FREE SOLDERINGSuccessful soldering results have been obtained using Multicore® 96S flux-cored solder, which has been specially developed to provide a lead-freesubstitute for tin/lead cored solder wire in all hand soldering operations. Minoradjustments to soldering temperatures will be required, but the resultant solderjoint will perform as well as tin/lead solder joints. There are numerous othersuppliers of lead-free solders and each Morgan Electro Ceramics site has its ownpreference. Therefore, it is recommended to contact the specific site for moredetailed information on solder recommendations.

SOLDERING IRON TIP LIFELead-free solder alloys and their cored wire fluxes are both more aggressive tosoldering iron tips than tin lead cored wire. As a result, tip life can be significantlyshortened. The tip life will depend to a large extent on the soldering temperatureused. As a general rule, a 10°C increase in temperature will halve tip life.However, manufacturers are currently introducing tips designed for extended lifeunder these conditions. Lead-free is less forgiving and the right tip for the job willgo a long way in preventing defects. Choose a solder tip which has enough heatdelivering capacity. Fine point tips cannot be used in all applications and in somecases a tip such as a chisel type is best suited to deliver sufficient heat to the partsto be soldered. Tip life will be reduced with lead-free solders and it is importantto choose tips really designed for lead-free soldering. Many tips are only tinnedwith lead-free solder and the iron plating is no different than traditional solderingtips. High tin solders like to dissolve iron and this reduces tip life.

TYPE OF SOLDERING IRONSoldering irons of various types are available. The main differences are in theheat output available and the accuracy of the temperature control. Oldertypes of soldering iron use a method of temperature control that results inlarge variations in tip temperature. At worst this can result in the solderfreezing at the lowest temperature and being too hot for some componentsat the highest temperature.

Improved results can be achieved with lead-free solders if modern solderingirons with good tip temperature control are used. Modern irons are availablewith higher power ratings, which itself is beneficial, but an ability to maintaintemperature and minimize fluctuation during soldering is more important asthis will enable operators to use a lower tip temperature.

HAND SOLDERINGFor operators used to working withtin-lead solders, hand soldering isoften controlled by specifying thesoldering iron's tip temperature.

However, as lead-free alloys havemuch higher melting points than tin-lead formulas, resulting in a significantlynarrower process window, a morecomprehensive set of parametersmust be defined. The key in reducingoperator issues and reduced wettingresides in the optimization of the

soldering process. To avoid issues use a flux content of 2-3% by weight in thesolder wire, use a solder tip temperature of 270-320°C. The main issuesencountered with lead-free hand-soldering are cold solder joints, poor wettingand de-wetting. These can be avoided.

A step-by step process transition would be as follows:• Ensure the tips are designed for lead-free• Ensure the flux content in the wire is a least 2% wt/wt• Use lead free tips with the longest life• Ensure the parts are easily solderable with the chosen flux• Avoid prolonged contact times• Avoid needless reworking of the joint• Avoid the use of additional liquid flux

The picture bottom left illustrates a typical lead free solder joint. This joint wasobtained using a temperature regulated soldering station with a lead free chiseltip. Different temperature settings on the solder tip were used to obtain thisjoint result.

EPOXY BONDIn heat sensitive applications it isoften necessary to observeparticular attention to the heattreatment process for theconnection joint.

Soft piezoelectric materials suchas PZT5K1, PZT5H1 or ofsimilar characteristics have a lowCurie temperature, hencemaking it more susceptible todepolarisation. Silver conductiveepoxies are a good alternative totraditional soldering techniques.

They typically come in the form of a two part composition; often requiring amixing ratio of 1:1 which is more suitable in a production environment. To ensurea high strength bond is achieved, thoroughly clean the surface with acetone orequivalent cleaning agent, allowing it to dry before applying the epoxy. Consultthe manufacturer’s technical datasheet if curing of the epoxy is required.

ELECTRODE SPUTTERINGMEC-Bedford offers in-house RF/DC sputtering of Gold/Nichrome, Nichrome,Silver, Aluminium and others upon request that can be supplied at varying filmthicknesses from 100Å to 20,000Å with a film uniformity of ±15%.

Film characterisation includes:

1. Thickness measurement via X-Ray Fluorescence (XRF) and/or surfaceprofilometer.

2. Resistivity measurement via four point probe and

3. Adhesion test.

The sputtering is done in a class 1000 clean room environment and adaptedfor high volume production.

ELECTRODES

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Figure 21: Typical Lead-free solder joint

Figure 22: Typical Silver conductive epoxy joint

SENSORSMorgan’s range of custom designed sensors find applications in many marketsin particular Medical, Industrial and Aerospace. Key applications include level,flow, vibration and dynamic pressure measurement. The sensing principals

used in Morgan sensors are either acoustic(active) and/or piezoelectric (passive).

SENSOR TYPES INCLUDE:• Ultrasonic Sensors• Accelerometers (passive)• Blood pressure sensor• Wheel balancing• Impact Sensors

Electronics form a key part of every sensor and MEC offer sensors comprisingof the sensing element only or design incorporating a level of electronicsintegration. Electronics design and manufacture is done in co-operation withour partner companies which include APEX in the USA and others in Europe.

ULTRASONIC SENSORSUltrasound Sensors use either time of flightmeasurement, Doppler or acoustic transmissionprinciples to measure a wide range ofparameters. Morgan’s considerable expertise inkey technologies for ultrasonic sensors is used todesign custom sensors for OEM applications.Morgan’s Engineers have expert knowledge ofthe fundamentals such as acoustics, matching

layers, damping and adhesive technology which are all key to good transducerdesign. A large portfolio of materials is used to design the optimum sensor in termsof acoustics, electro-mechanical properties and environmental resistance.

ACCELEROMETERSMorgan’s stable and high sensitivity materialsform an excellent basis of accelerometers. Thepiezo electric materials can be used in eithercompression or shear mode to form single ormulti-axis accelerometers. Accelerometers canbe housed in standard housing (e.g. transistor

cans) or custom made packages. Morgan’s bimorph materials can also be usedwhere increased sensitivity is required.

ARTERIAL PRESSURE TRANSDUCERThe Arterial Pressure Transducer (APT) is apiezoelectric transducer that provides fast,accurate blood pressure readings. Like all ofMorgan Electro Ceramics’ ultrasonic transducers,it has been designed using our world leadingpiezo materials.

IMPACT SENSORSImpact sensors use the piezo-electric effect tosense forces (dynamic) and rate of forceapplication. Example applications of impactsensors are coin validation equipment andfirmness testing (e.g. fruit). In designing thesesensors great care is taken to ensure that the signalresponse is consistent in a variety of conditions,angle of impact, temperature etc.

WHEEL BALANCING SENSORSMorgan’s over-moulded sensors for wheelbalancing can be found in many garageworkshops around the world. Many OEMmanufactures of wheel balancing equipmenthave found that Morgan’s design offers andexcellent solution in terms of value for money,robustness and accuracy. These over-mouldedsensors are available in a number of versions.

Transducers are generally supplied with exposed (solderable) connectors. Uponrequest custom versions with either IDC or flying leads (with or withoutconnector) can be manufactured.

TRANSDUCER & SENSOR MANUFACTURINGAll of our transducer and sensor manufacturing facilities are ISO 9000:2000certified and many are also certified to ISO 14001:2004.

PROCESSES & CAPABILITIES INCLUDE:

• Prototype assemblies

• Small to large volume manufacture

• Custom assembly

• Clean room facilities available• Wire bonding / pulse soldering

• Thermal cycling

• Humidity chamber

• Encapsulation (Thermoplast + Thermoset)

TRANSDUCER TESTINGThe testing of electrical properties of resonating structures requires considerableexpertise and sophisticated equipment. Facilities such as these are availablethroughout our design and production process.

MEASUREMENT TOOLS USED INCLUDE:• Impedance Analyser (4194A and 4294A)

• Laser Vibrometer

• Acoustic characterisation (tank test) / Echo Response Rigs

• Sound pressure measurement / Beam characterisation

• Shaker table, charge sensitivity measurement (accelerometers)

• Power meter

• Optical inspection including SEM and Vision CMM

PIEZOELECTRIC BIMORPHSWith a history in piezo bimorphs extendingsome 45 years to the pioneering days of thetechnology, MEC brings a wealth of experiencein the development of customized high precisionpiezo bimorphs components – resulting in realadded-value for our customers. Today you willfindMorgan Electro Ceramics piezo bimorphs ina host of specialist application areas, including

ultrasonic atomizers, transducers, printing technologies, pneumatic valves, textilemachinery and many more. The bimorphs are available in a range of sizes from 6to 74mm in length and 1 to 43mm in width, to reflect the variety of applicationsin which they can be used.

SERIES & PARALLEL BIMORPHS: HIGH SENSITIVITY & COST EFFICIENT

Examples of applications:

• Sensor systems (airbag)

• Printing technologies

• Ultrasonic atomizers

• Ultrasonic transducers

• Viscosity measurement systems

• Flow measurement systems

CARBON-FIBRE OR METAL REINFORCED BIMORPHS:HIGH FORCE/DEFLECTION RATIO AND EXTREMELY LONG LIFE-TIME

Examples of applications:

• Pneumatic valves for industrial and automotive applications

• Valves in medical applications

• Insulin pumps

• Braille keys for the blind

• Energy harvesting in car-tyres

• Textile machinery

• Optical switches

Many applications require displacements far greater than are possible withsimple PZT transducers operating in the d33 or d31 modes. Moreover, thevoltages required to produce these displacements are very high, and becausethey present a considerable mismatch to air, these elements are unsuitablefor use as electro-acoustic transducers. A much more compliant structureoperating in the d31 mode is the flexure element, the simplest form of which isthe bilaminar cantilever or bimorph. This consists of two thin PZT strips bondedtogether. Bimorphs are usually mounted as a cantilever and usually operate inthe d31 mode as shown on figure 23 & 24.

In a series bimorph, PZT strips are connectedto the voltage source in series (See figure 23),and in a parallel bimorph strips are individuallyconnected to the voltage source (See figure 24).

In the series bimorph, one of the PZT stripswill always be subject to a voltage opposite tothe polarising voltage, so there is always adanger of depolarisation. This is also true to

the parallel bimorph configuration of figure 25, but if it is connected as shownin figure 26, both strips will be driven in the polarisation direction, therebyavoiding drift in characteristics caused by depolarisation.

PRACTICAL DESIGNDATA FOR PZT500 SERIES FLEXURE ELEMENTS

Table 6: Summary of equations for bimorphs

PZT FLEXURE ELEMENTS: BIMORPH

27

TRANSDUCERS & SENSORS

26

Lt: Total lengthF: Force on tipW: WidthL: Free lengthh: Total thicknessz: Deflection of tipField Strength: max 500V/mm

Figure 26: Flexure element (Bimorph)

Figure 25

Figure 24

Figure 23

PARAMETER PARALLEL BIMORPH SERIES BIMORPH UNIT

DEFLECTION m/V

BENDING m/N

RESONANCE HzFREQUENCY

CHARGE OUTPUT C/N

CAPACITANCE F

VOLTAGE OUTPUT V/N

Axial mode multilayer d33-mode actuators achieve higher displacements butalso retain high blocking forces which are proportional to cross-sectional areaas illustrated in the figure 32 underneath.

TRANSVERSAL MODE (D31) ACTUATORSMultilayer actuators (figure 33) can be produced with layer thicknesses as low as20-40µm. The manufacturing method is completely different from the classicalprocess of sawing and electroding individual discs or plates. Because of the verythin layers of PZT, an electrical field strength of about 1kV/mm can easily bereached for a drive voltage as low as around 50V. The elongation per unit lengthor height is roughly the same as for of “classical” actuators. The difference is thatthe effect is reached for a much lower voltage. The performance of a transversald31-mode type is shown in figure 34. Note that the element shortens for a drivevoltage in the polarisation direction.

MULTILAYER ACTUATORS

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MULTILAYER FLEXURE MODE ACTUATORSThe use of very thin piezoelectric layers in flexure elements requires muchlower driving voltages than classical bimorph actuators.

Basically these elements can be built up three ways:

• Gluing a d31 actuator onto an inactive substrate, like a metal strip• Combining a d31 actuator with an unpolarised PZT layer• Combining layers of piezoelectric ceramic with an intricate electrode structureso that the layers expand or contract like a classical bimorph element.

Figure 27: below illustrates a multilayer parallel bimorph element.

Since the maximum strain is around 5x10-4 for 1kV/mm (as with discreteflexure elements), the general rule and formulas in this section also apply tomultilayer elements.

Figure 28 below shows the performance of a typical multilayer flexure modeactuator.

AXIAL MODE MULTILAYER ACTUATORS (D33-MODE)As with “classical”, axially-stacked actuators, the strain in the direction ofpolarisation is twice as large as it is in the transverse direction. However, toget a large absolute elongation, the dimension of the actuator in the directionof polarisation must be large as well.

For the multilayer process the thickness is currently limited to about 2mm.Figure 29 below shows the structure of such an element.

Since the maximum strain is about 1X10-3 at 50V supply voltage, the absoluteincrease of its thickness will be about 2�m.

For most practical applications it is necessary to stack several of theseelements to form a so called multilayer stacked actuator as illustrated in thefigure 30 below.

MULTILAYER ACTUATORS

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Figure 27: Multilayer parallel bimorph element

Figure 29: Axial mode multilayer actuator

Figure 28: Deflection of flexure mode actuator as a function of applied voltage

Figure 30: Various examples of stacked d33-mode actuators

Figure 31: Performance of a multilayer d33-mode actuator Figure 34: Performance of a multilayer d31-mode actuator

Figure 33: Tranversal mode (D31) multilayer actuator

Bimorph ActuatorCombination of 2d31 actuators

Poling direction

Electrical field

Displacment

Figure 32: Blocking force of square stacks

NAVY 1I TYPE PIEZOELECTRIC CERAMICS

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NAVY 1 TYPE PIEZOELECTRIC CERAMICS

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Typical Values measured at 20°C ±1°C are provided for design information only. Standard tolerances are approximately ±20% of these values.Material properties are measured according to standard IEEE and DOD definitions and measuring techniques.

PROPERTY SYMBOL UNIT PZT5A1 PZT5A2 PZT5A3 PZT5A4NO OF DAYS AFTER POLING 1 1 1 1

ELECTRICAL - LOW FIELDRelative Permittivity 1875 1700 1700 1850Relative Permittivity - 1730 1730 1650Dielectric Loss tan � 0.02 0.02 0.02 0.017Resistivity (at 25oC) � el �m 1012 - - 5010Resistivity (at 100oC) � el �m - - - -Resistivity (at 200oC) � el �m - - - -

ELECTRICAL - HIGH FIELDIncrease in @ 2KV/cm % - - - -Dielectric Loss @ 2KV/cm tan � - - - -Increase in @ 4KV/cm % - - - -Dielectric Loss @ 4KV/cm tan � - - - -

ELECTRO-MECHANICALCoupling Factors k� 0.62 0.60 0.60 0.66

k15 0.69 0.69 0.69 0.68k31 -0.34 -0.34 -0.34 -0.37k33 0.67 0.71 0.71 0.72kt 0.45 - - -

Charge Constants d33 x 10-12 C/N 409 374 374 460or Strain Constants d31 x 10-12 C/N or m/V -176 -171 -171 -195

dh x 10-12 C/N 58 32 32 -d15 x 10-12 C/N or m/V - 585 585 550

Voltage Constants g33 x 10-3 Vm/N 25.7 24.8 24.8 28or Stress Constants g31 x 10-3 Vm/N -11 -11.4 -11.4 -13

gh x 10-3 Vm/N 3.6 2 2 -g15 x 10-3 Vm/N - 38.2 38.2 37dhgh x 10-15 - 64 64 -

Frequency Constants N� Hz.m 2000 1960 1960 1970N1 Hz.m 1370 1400 1400 1400N3 Hz.m 1410 - - 2060N5 Hz.m - - - 900Na Hz.m - 1845 1845 -

N3t or N33 Hz.m - 1880 1880 -Ns Hz.m 1465 - - -

Hoop or Nc Hz.m 930 890 890 -Nt Hz.m 1940 - - -

Compressive Strength 106 Pa - - - >600Tensile Strength 106 Pa - - - 100Quality Factor Qm 60 75 75 80

MECHANICALCompliances SE33 x 10-12 m2/N 17.2 18.8 18.8 18

SE11 x 10-12 m2/N 16.7 16.4 16.4 16SE12 x 10-12 m2/N -5.2 - - -SE13 x 10-12 m2/N - - - -SE55 x 10-12 m2/N - - - 45SE66 x 10-12 m2/N - - - -SD33 x 10-12 m2/N 9.4 9.4 9.4 -SD11 x 10-12 m2/N 15 14.4 14.4 -SD12 x 10-12 m2/N -7.1 - - -S66 x 10-12 m2/N 43.7 - - -YE33 x 1010 N/m2 - 5.3 5.3 -YE11 x 1010 N/m2 - 6.1 6.1 -YD33 x 1010 N/m2 - 10.6 10.6 -YD11 x 1010 N/m2 - 6.9 6.9 -

Poisson’s Ratio - - - 0.35Density � kg/m3 7750 - 7700 7900

THERMAL DATACurie Temperature Tc °C 370 374 365 360Approx. Operating Temp. °C - 250 250 -Specific Heat J/kg K - - - 420Thermal Conductivity W/m K - - - 1.2Young's Modulus E Gpa - - - -Internal Friction Q-1 x 10-4 - - - -

TIME STABILITY Relative change perCoupling Factor k� time decade % -0.40 -0.10 0.00 -0.10Capacitance C -1.60 - - -Permittivity -0.90 -0.90 -2.00Frequency f 0.20 - +0.1

d33 - -2.90 -2.90 -Time Constant � T/33 (25oC) minutes - - - >100

N� - - +0.1 -Quality Factor Qm - - - +0.1Dielectric Loss Factor tan � - - - -0.1

Typical Values measured at 20°C ±1°C are provided for design information only. Standard tolerances are approximately ±20% of these values.Material properties are measured according to standard IEEE and DOD definitions and measuring techniques.

PROPERTY SYMBOL UNIT PZT401 PZT402 PZT403 PZT404 PZT405 PZT406NO OF DAYS AFTER POLING 1 1 1 1 1 1

ELECTRICAL - LOW FIELDRelative Permittivity 1470 1200 1350 1450 1450 1325Relative Permittivity - - 1475 - - -Dielectric Loss tan � 0.002 0.003 0.003 0.004 0.003 0.0035Resistivity (at 25oC) � el �m 1010 >1010 - - - 1010

Resistivity (at 100oC) � el �m - 108.5 - - - -Resistivity (at 200oC) � el �m - 105.5 - - - -

ELECTRICAL - HIGH FIELDIncrease in @ 2KV/cm % 5.1 - - - - -Dielectric Loss @ 2KV/cm tan � 0.01 - - - - -Increase in @ 4KV/cm % 12.7 - 25 - 25 -Dielectric Loss @ 4KV/cm tan � 0.02 - - - - -

ELECTRO-MECHANICALCoupling Factors k� 0.60 0.56 0.58 0.60 0.62 0.61

k15 0.70 0.71 0.60 - - -k31 -0.35 -0.33 -0.33 -0.34 - -0.34k33 0.67 0.70 0.68 0.71 - 0.70kt - - - - - -

Charge Constants d33 x 10-12 C/N 315 285 315 315 350 315or Strain Constants d31 x 10-12 C/N or m/V -132 -122 -135 -135 - -130

dh x 10-12 C/N 51 41 45 45 - -d15 x 10-12 C/N or m/V 511 495 - - - -

Voltage Constants g33 x 10-3 Vm/N 26.8 24.8 26.4 24.6 27.3 27or Stress Constants g31 x 10-3 Vm/N -12 -10.6 -10.5 -10.5 - -11

gh x 10-3 Vm/N 2.8 3.7 3.6 3.6 - -g15 x 10-3 Vm/N - 38 - - - -dhgh x 10-15 143 152 162 162 - -

Frequency Constants N� Hz.m 2190 2180 2120 2110 2160 2200N1 Hz.m 1636 1650 1515 1515N3 Hz.m 1576 - - - - 2015Na Hz.m - 2060 - - - -

N3t or N33 Hz.m - 2000 2000 - - -Ns Hz.m 1800 - - - - -

Hoop or Nc Hz.m 1030 1040 990 990 - -Nt Hz.m 2080 - - - - -

Compressive Strength 106 Pa - - - - - >600Tensile Strength 106 Pa - - - - - 80Quality Factor Qm 600 500 600 600 - 750

MECHANICALCompliances SE33 x 10-12 m2/N 15.6 15.5 16.8 16.8 - 15

SE11 x 10-12 m2/N 12.7 12.3 13.3 13.3 - 13SE12 x 10-12 m2/N -3.86 - - - - -SE13 x 10-12 m2/N 5.76 - - - - -SE55 x 10-12 m2/N 39.2 - - - - -SE66 x 10-12 m2/N - - - - - -SD33 x 10-12 m2/N 7.76 7.9 - - - -SD11 x 10-12 m2/N 11.1 10.9 11.8 11.8 - -SD12 x 10-12 m2/N -5.44 - - - - -S66 x 10-12 m2/N - - - - - -YE33 x 1010 N/m2 - 6.6 5.9 5.9 - -YE11 x 1010 N/m2 - 8.2 7.5 7.5 - -YD33 x 1010 N/m2 - 12.6 - - - -YD11 x 1010 N/m2 - 9.9 8.5 8.5 - -

Poisson’s Ratio - 0.31 0.31 0.31 - 0.3Density � kg/m3 7600 7600 7600 7600 7500 7800

THERMAL DATACurie Temperature Tc °C 330 320 320 325 300 325Approx. Operating Temp. °C - - 200 - - -Specific Heat J/kg K - - - - - 420Thermal Conductivity W/m K - - - - - 1.2Young's Modulus E Gpa - - - - - -Internal Friction Q-1 x 10-4 - - - - - -

TIME STABILITY Relative change perCoupling Factor k� time decade % -1.70 -1.70 -2.10 -2.10 -2.50Capacitance C -4.60 - - - - -Permittivity - -2.50 -4.60 -4.60 - -6.00Frequency f 1.00 - - - - -

d33 - -3.40 -3.40 -3.40 - -Time Constant Seconds - - - - - -

N� - +0.8 +1.2 +1.2 - +1.5

r 33T

r 33T

33T

r 33T

r 33T

33T

r 33T

r 11T

r 33T

r 11T

NAVY V & V1 TYPE PIEZOELECTRIC CERAMICS

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NAVY 1I1 TYPE PIEZOELECTRIC CERAMICS

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PROPERTY SYMBOL UNIT PZT801 PZT802 PZT804 PZT805 PZT806 PZT807NO OF DAYS AFTER POLING 1 1 1 1 1 1

ELECTRICAL - LOW FIELDRelative Permittivity 1000 1150 1050 1000 1250 1150Relative Permittivity - 1290 - - - 1190Dielectric Loss tan � 0.004 0.003 0.001 0.002 0.003 0.0016Resistivity (at 25oC) � el �m 1010 1010 - 1010 1013 1012

Resistivity (at 100oC) � el �m - - - - - -Resistivity (at 200oC) � el �m - - - - - -

ELECTRICAL - HIGH FIELDIncrease in @ 2KV/cm % - - - - 1.9 -Dielectric Loss @ 2KV/cm tan � - - - - 0.004 -Increase in @ 4KV/cm % - - - - 4.7 3.6Dielectric Loss @ 4KV/cm tan � 0.009 0.015 0.008 0.01 0.006

ELECTRO-MECHANICALCoupling Factors k� 0.51 0.54 0.55 0.53 0.55 0.55

k15 0.55 0.55 - - - -k31 -0.30 -0.30 - -0.30 -0.31 -0.29k33 0.64 0.64 - 0.66 0.71 0.69kt - - - - 0.45 0.47

Charge Constants d33 x 10-12 C/N 225 250 250 230 280 260or Strain Constants d31 x 10-12 C/N or m/V -97 -97 - -100 -104 -92.75

dh x 10-12 C/N 31 31 - - 79 44.5d15 x 10-12 C/N or m/V 330 300 - - - 294

Voltage Constants g33 x 10-3 Vm/N 25.4 24.6 26.9 27 26.4 25.08or Stress Constants g31 x 10-3 Vm/N -10.9 -10.9 - -11 -10.9 -10.11

gh x 10-3 Vm/N 3.6 3.6 - - 8.3 4.86g15 x 10-3 Vm/N -28.9 -28.9 - - - 28.82dhgh x 10-15 112 112 - - - -

Frequency Constants N� Hz.m 2340 2285 2245 2350 2155 2320N1 Hz.m 1700 1700 - - 1660 -N3 Hz.m - - - 2050 1555 -Na Hz.m 2000 2000 - - - -

N3t or N33 Hz.m 2070 2070 - - - -Ns Hz.m - - - - 1780 -

Hoop or Nc Hz.m 1070 1070 - - 1010 1080Nt Hz.m - - - - 2060 2030

Compressive Strength 106 Pa - >517 - >600 - -Tensile Strength 106 Pa - 75.8 - 80 - 75Quality Factor Qm 1000 1000 - 1000 1200 1200

MECHANICALCompliances SE33 x 10-12 m2/N 13.5 13.5 - 13 14.7 15.65

SE11 x 10-12 m2/N 11.5 11.5 - 11 11.7 10.9SE12 x 10-12 m2/N - - - - -3.6 -3.3SE13 x 10-12 m2/N - - - - - -4.8SE55 x 10-12 m2/N - - - - - 31.4SE66 x 10-12 m2/N - - - - - 28.3SD33 x 10-12 m2/N 8.5 8.5 - - 7.4 8.2SD11 x 10-12 m2/N 10.1 10.1 - - 10.8 9.9SD12 x 10-12 m2/N - - - - -4.8 -4.2S66 x 10-12 m2/N - - - - 30.7 -YE33 x 1010 N/m2 7.4 7.4 - - - -YE11 x 1010 N/m2 8.7 8.7 - - - -YD33 x 1010 N/m2 11.8 11.8 - - - -YD11 x 1010 N/m2 9.9 9.9 - - - -

Poisson’s Ratio - - - 0.3 - -Density � kg/m3 7600 7500 7450 7800 7600 7650

THERMAL DATACurie Temperature Tc °C 300 300 300 300 300 300Approx. Operating Temp. °C - 175 - - - -Specific Heat J/kg K - - - 420 - -Thermal Conductivity W/m K - - - 1.2 - -Young's Modulus E Gpa - - - - - 88.6Internal Friction Q-1 x 10-4 - - - - - 8.6

TIME STABILITY Relative change perCoupling Factor k� time decade % -2.10 -1.50 - -2.00 -2.10 -1.50Capacitance C - - - - -4.10 -3.50Permittivity -4.00 -4.00 - -4.50 - -Frequency f 0.90 0.90 - 1.00 1.10 0.75

d33 -6.30 -6.30 - - - -Time Constant Seconds 100 (at 25

oC) 100 (at 25

oC) - - - -

Typical Values measured at 20°C ±1°C are provided for design information only. Standard tolerances are approximately ±20% of these values.Material properties are measured according to standard IEEE and DOD definitions and measuring techniques.

PROPERTY SYMBOL UNIT PZT5J1 PZT5H1 PZT5H2NO OF DAYS AFTER POLING 1 1 1

ELECTRICAL - LOW FIELDRelative Permittivity 2600 3400 3400Relative Permittivity - - -Dielectric Loss tan � 0.02 0.018 0.025Resistivity (at 25oC) � el �m - - >1011

Resistivity (at 100oC) � el �m - - 1011

Resistivity (at 200oC) � el �m - - 1010

ELECTRICAL - HIGH FIELDIncrease in @ 2KV/cm % - - -Dielectric Loss @ 2KV/cm tan � - - -Increase in @ 4KV/cm % - - -Dielectric Loss @ 4KV/cm tan � - - -

ELECTRO-MECHANICALCoupling Factors k� 0.60 0.60 0.65

k15 0.63 - 0.68k31 -0.36 -0.35 -0.39k33 0.69 0.72 0.75kt - 0.50 -

Charge Constants d33 x 10-12C/N 500 620 593or Strain Constants d31 x 10-12 C/N or m/V -220 -250 -274

dh x 10-12 C/N 60 125 45d15 x 10-12 C/N or m/V 670 - 741

Voltage Constants g33 x 10-3 Vm/N 21.7 21.9 19.7or Stress Constants g31 x 10-3 Vm/N -9.6 -8.7 -9.1

gh x 10-3 Vm/N 2.5 4.4 1.5g15 x 10-3 Vm/N 35 - 26.8dhgh x 10-15 150 - 68

Frequency Constants N� Hz.m 1980 1975 1965N1 Hz.m 1450 1375 1420N3 Hz.m - 1785 -Na Hz.m - - 1930

N3t or N33 Hz.m - - 2000Ns Hz.m - 1430 -

Hoop or Nc Hz.m 910 920 890Nt Hz.m - 1895 -

Compressive Strength 106 Pa - - -Tensile Strength 106 Pa - - -Quality Factor Qm 75 65 65

MECHANICALCompliances SE33 x 10-12 m2/N 22.7 21.9 20.8

SE11 x 10-12 m2/N 16.2 17.7 16.4SE12 x 10-12 m2/N - -5.7 -SE13 x 10-12 m2/N - - -SE55 x 10-12 m2/N - - -SE66 x 10-12 m2/N - - -SD33 x 10-12 m2/N - 10.5 9SD11 x 10-12 m2/N 14.1 15.5 14.1SD12 x 10-12 m2/N - -7.6 -S66 x 10-12 m2/N - 48.5 -YE33 x 1010 N/m2 4.4 - 4.8YE11 x 1010 N/m2 6.2 - 6.2YD33 x 1010 N/m2 - 11.1YD11 x 1010 N/m2 7.1 - 7.1

Poisson’s Ratio 0.31 - -Density � kg/m3 7400 7400 7450

THERMAL DATACurie Temperature Tc °C 250 200 195Approx. Operating Temp. °C 140 - 110Specific Heat J/kg K - - -Thermal Conductivity W/m K - - -Young's Modulus E Gpa - - -Internal Friction Q-1 x 10-4 - - -

TIME STABILITY Relative change perCoupling Factor k� time decade % -0.30 -0.20 -0.20Capacitance C - -1.50 -Permittivity -1.10 - -0.60Frequency f - 0.30 -

d33 -4.00 - -3.90Time Constant Seconds - - -

N� +0.2 - +0.3

Typical Values measured at 20°C ±1°C are provided for design information only. Standard tolerances are approximately ±20% ofthese values. Material properties are measured according to standard IEEE and DOD definitions and measuring techniques.

r 33T

r 33T

r 33T

r 11T

33T

r 33T

r 33T

33T

r 33T

r 11T

CUSTOM PIEZOELECTRIC CERAMICS

35

CUSTOM PIEZOELECTRIC CERAMICS

34

Typical Values measured at 20°C ±1°C are provided for design information only. Standard tolerances are approximately ±20% of these values.Material properties are measured according to standard IEEE and DOD definitions and measuring techniques.

PROPERTY SYMBOL UNIT PZT701 PZT702 PZT703 PZT407 PT1 PZT601NO OF DAYS AFTER POLING 1 1 1 1 1 1

ELECTRICAL - LOW FIELDRelative Permittivity 425 1200 1100 1225 210 640Relative Permittivity - 1700 - 1400 240 750Dielectric Loss tan � 0.01 0.005 0.029 0.0025 0.02 0.005Resistivity (at approx 25oC) � el �m >1011 - 5010 1010 - -Resistivity (at 100oC) � el �m 1011 - - - - -Resistivity (at 200oC) � el �m 1010 - - - - -

ELECTRICAL - HIGH FIELDIncrease in @ 2KV/cm % - - - - -Dielectric Loss @ 2KV/cm tan � - - - - -Increase in @ 4KV/cm % - - - - -Dielectric Loss @ 4KV/cm tan � - - - - -

ELECTRO-MECHANICALCoupling Factors k� 0.52 0.48 0.63 0.64 <0.020 0.52

k15 0.68 - 0.68 0.70 0.36 0.69k31 -0.3 -0.28 0.37 0.38 <0.020 0.30k33 0.67 - 0.73 0.74 0.54 0.67kt - - - - - 0.48

Charge Constants d33 x 10-12 C/N 153 225 340 325 68 170or Strain Constants d31 x 10-12 C/N or m/V -60 -100 -150 -150 -3 -64

dh x 10-12 C/N 33 25 - - 62 -d15 x 10-12 C/N or m/V 360 - 500 480 70 310

Voltage Constants g33 x 10-3 Vm/N 41 21 30 30 37 37or Stress Constants g31 x 10-3 Vm/N -16 -9.6 -10 -12 -2 -14

gh x 10-3 Vm/N 9 - - - 33 -g15 x 10-3 Vm/N 50 - 33 39 34 45dhgh x 10-15 297 - - - 2046 -

Frequency Constants N� Hz.m 2340 2260 2100 2175 2870 2450N1 Hz.m 1750 1625 1500 1620 n/a -N3 Hz.m - - - 2000 - -N5 Hz.m - - 920 950 - -Na Hz.m 2050 - - - - -

N3t or N33 Hz.m 2100 - - - 2145 1750Ns Hz.m - - - - - -

Hoop or Nc Hz.m 1070 1040 - - - -Nt Hz.m - - - - - 2150

Compressive Strength 106 Pa - - >600 >600 - -Tensile Strength 106 Pa - - 80 80 - -Quality Factor Qm 600 500 80 1200 1100 1000

MECHANICALCompliances SE33 x 10-12 m2/N 13.9 - - 15 8.6 13.5

SE11 x 10-12 m2/N 10.7 10.9 15 12 7.4 10SE12 x 10-12 m2/N - - - - - -3.1SE13 x 10-12 m2/N - - - - - -6.6SE55 x 10-12 m2/N - - 38 37 - 30.4SE66 x 10-12 m2/N - - - - - 26SD33 x 10-12 m2/N 7.9 - - - 6.1 7.4SD11 x 10-12 m2/N 9.7 10 - - 7.3 9SD12 x 10-12 m2/N - - - - - -4S66 x 10-12 m2/N - - - - - 26YE33 x 1010 N/m2 7.2 - - - 11.6 7.4YE11 x 1010 N/m2 9.3 9.2 - - 13.5 9.8YD33 x 1010 N/m2 10.3 - - - 16.4 13YD11 x 1010 N/m2 12.7 10 - - 13.7 11

Poisson’s Ratio 0.31 0.31 0.3 0.3 - 0.31Density � kg/m3 7700 7600 7800 7900 6900 7700

THERMAL DATACurie Temperature Tc °C 350 325 270 315 255 300Approx. Operating Temp. °C 210 - - - 130 -Specific Heat J/kg K - - 420 420 - -Thermal Conductivity W/m K - - 1.2 1.2 - -Young's Modulus E Gpa - - - - - -Internal Friction Q-1 x 10-4 - - - - - -

TIME STABILITY Relative change perCoupling Factor k� time decade % 0.00 0.01 -0.50 -1.50 - -Capacitance C - - - - - -Permittivity 0.06 0.03 -0.50 1.00 - -Frequency N� -0.05 0.02 0.50 0.50 - -

d33 - - - - - -Time Constant � T/3 (25oC) minute - - >250 >7 - -Quality factor Qm - - - 10 - -Dielectric Loss factor tan � - - - -10 - -

Typical Values measured at 20°C ±1°C are provided for design information only. Standard tolerances are approximately ±20% of these values.Material properties are measured according to standard IEEE and DOD definitions and measuring techniques.

PROPERTY SYMBOL UNIT PZT501 PZT502 PZT503 PZT504 PZT505 PZT506 PZT507 PZT508NO OF DAYS AFTER POLING 1 1 1 1 1 1 1

ELECTRICAL - LOW FIELDRelative Permittivity 2000 1950 2100 2000 2600 2250 4400 3900Relative Permittivity - - 1800 - - - 3300 -Dielectric Loss tan � 0.02 0.02 0.02 0.015 0.019 0.02 0.016 0.02Resistivity (at approx 25oC) � el �m >1011 - 5010 5010 5010 1010Resistivity (at 100oC) � el �m 1011 - - - - - - -Resistivity (at 200oC) � el �m 1010 - - - - - - -

ELECTRICAL - HIGH FIELDIncrease in @ 2KV/cm % - - - - - - - -Dielectric Loss @ 2KV/cm tan � - - - - - - - -Increase in @ 4KV/cm % - - - - - - - -Dielectric Loss @ 4KV/cm tan � - - - - - - - -

ELECTRO-MECHANICALCoupling Factors k� 0.6 0.65 0.68 0.64 0.72 0.7 0.75 0.71

k15 0.63 - 0.66 - - - - 0.72k31 -0.34 -0.35 -0.38 -0.37 - - -0.39 0.41k33 0.66 - 0.75 0.74 - - 0.8 -0.75kt - - - - - - - -

Charge Constants d33 x 10-12 C/N 405 450 500 450 610 545 820 720or Strain Constants d31 x 10-12 C/N or m/V -185 -195 -215 -200 -270 -225 -360 -315

dh x 10-12 C/N 95 60 - - - - - 90d15 x 10-12 C/N or m/V 564 - 515 - - - - 750

Voltage Constants g33 x 10-3 Vm/N 22.9 25 24 25 - - 20 18.5or Stress Constants g31 x 10-3 Vm/N -10.5 -11.5 -10 -12 - - -10 -9

gh x 10-3 Vm/N 1.9 2 - - - - - 0.5g15 x 10-3 Vm/N 36.4 - 33 - - - - -dhgh x 10-15 181 120 - - - - - 45

Frequency Constants N� Hz.m 1950 1930 1975 2000 1900 1940 1925 1950N1 Hz.m 1420 1400 1450 - - - 1400 1420N3 Hz.m - - 1850 1900 - - 1800 1880N5 Hz.m - - 930 - - - - -Na Hz.m - - - - - - - -

N3t or N33 Hz.m - - - - - - - -Ns Hz.m - - - - - - - -

Hoop or Nc Hz.m 890 78 - - - - - -Nt Hz.m - - - - - - - -

Compressive Strength 106 Pa - - >600 >600 - - >600 -Tensile Strength 106 Pa - - 80 80 - - 80 -Quality Factor Qm 75 80 75 75 60 65 65 55

MECHANICALCompliances SE33 x 10-12 m2/N - - 18 19 - - 20 22

SE11 x 10-12 m2/N 16.4 16.1 15 15 16.5 15.5 16 16.4SE12 x 10-12 m2/N - - - - - - - -SE13 x 10-12 m2/N - - - - - - - -SE55 x 10-12 m2/N - - 39 - - - - -SE66 x 10-12 m2/N - - - - - - - -SD33 x 10-12 m2/N - - - - - - - 8.8SD11 x 10-12 m2/N 14.4 14.1 - - - - - 13.9SD12 x 10-12 m2/N - - - - - - - -S66 x 10-12 m2/N - - - - - - - -YE33 x 1010 N/m2 - - - - - - - 4.9YE11 x 1010 N/m2 6.1 6.2 - - - - - 6.1YD33 x 1010 N/m2 - - - - - - - 11YD11 x 1010 N/m2 6.9 7.1 - - - - - 7

Poisson’s Ratio 0.31 0.31 0.3 0.3 - - - -Density � kg/m3 7600 7800 7800 7800 7830 8000 7800 7900

THERMAL DATACurie Temperature Tc °C 330 350 285 270 285 300 165 208Approx. Operating Temp. °C - - - - - - - -Specific Heat J/kg K - - 420 420 - - 420 -Thermal Conductivity W/m K - - 1.2 1.2 - - 1.2 -Young's Modulus E Gpa - - - - - - - -Internal Friction Q-1 x 10-4 - - - - - - - -

TIME STABILITY Relative change perCoupling Factor k� time decade % 0.00 0.00 -0.50 -1.50 - - -0.60 -Capacitance C - - - - - - - -Permittivity -0.90 -3.60 -1.00 -2.00 - - -1.00 -Frequency N� 0.10 0.20 0.50 0.50 - - 0.30 -

d33 -2.90 -3.10 - - - - - -Time Constant � T/3 (25oC) minute - - >300 >25 - - >500 -Quality factor Qm - - - - - - -3.00 -Dielectric Loss factor tan � - - - - - - - -

r 33T

r 33T

r 33T

r 11T

33T

r 33T

r 33T

33T

r 33T

r 11T

SINGLE CRYSTAL MATERIALS

37

CUSTOM PIEZOELECTRIC CERAMICS

36

PROPERTY SYMBOL UNIT PZT5K1 PZT5K2 PZT5K4NO OF DAYS AFTER POLING 1 1 1

ELECTRICAL - LOW FIELDRelative Permittivity 6200 6200 7100Relative Permittivity - 5200 -Dielectric Loss tan � 0.02 0.02 0.02Resistivity (at approx 25oC) � el �m - - -Resistivity (at 100oC) � el �m - - -Resistivity (at 200oC) � el �m - - -

ELECTRICAL - HIGH FIELDIncrease in @ 2KV/cm % - - -Dielectric Loss @ 2KV/cm tan � - - -Increase in @ 4KV/cm % - - -Dielectric Loss @ 4KV/cm tan � - - -

ELECTRO-MECHANICALCoupling Factors k� 0.68 0.70 0.70

k15 - - -k31 -0.40 -0.42 -0.42k33 0.75 0.78 0.78kt - 0.50 0.49

Charge Constants d33 x 10-12 C/N 870 880 950or Strain Constants d31 x 10-12 C/N or m/V -370 -401 -410

dh x 10-12C/N 130 78 130d15 x 10-12 C/N or m/V - - -

Voltage Constants g33 x 10-3 Vm/N 15.8 16 15.1or Stress Constants g31 x 10-3 Vm/N -6.8 -7.1 -6.5

gh x 10-3 Vm/N 2.2 1.7 2.1g15 x 10-3 Vm/N - - -dhgh x 10-15 286 137 273

Frequency Constants N� Hz.m 1920 1880 1880N1 Hz.m 1380 - -N3 Hz.m - - -N5 Hz.m - - -Na Hz.m - - -

N3t or N33 Hz.m - - -Ns Hz.m - - -

Hoop or Nc Hz.m - - -Nt Hz.m - - -

Compressive Strength 106 Pa - - -Tensile Strength 106 Pa - - -Quality Factor Qm 65 68 60

MECHANICALCompliances SE33 x 10-12 m2/N 20.4 23.2 23.6

SE11 x 10-12 m2/N 16.4 16.6 16.4SE12 x 10-12 m2/N - - -SE13 x 10-12 m2/N - - -SE55 x 10-12 m2/N - - -SE66 x 10-12 m2/N - - -SD33 x 10-12 m2/N 8.9 9.1 9.24SD11 x 10-12 m2/N 14.7 13.7 13.6SD12 x 10-12 m2/N - - -S66 x 10-12 m2/N - - -YE33 x 1010 N/m2 4.9 4.3 4.2YE11 x 1010 N/m2 6.4 6 6.1YD33 x 1010 N/m2 - 10.9 10.8YD11 x 1010 N/m2 - 7.3 7.3

Poisson’s Ratio - - -Density � kg/m3 8200 8200 8200

THERMAL DATACurie Temperature Tc °C 160 150 137Approx. Operating Temp. °C - - -Specific Heat J/kg K - - -Thermal Conductivity W/m K - - -Young's Modulus E Gpa - - -Internal Friction Q-1 x 10-4 - - -

TIME STABILITY Relative change perCoupling Factor k� time decade % -0.50 - -Capacitance C -0.50 - -Permittivity - - -Frequency N� - - -

d33 - - -Time Constant � T/3 (25oC) minute - - -Quality factor Qm - - -Dielectric Loss factor tan � - - -

Typical Values measured at 20°C ±1°C are provided for design information only. Standard tolerances are approximately ±20% ofthese values. Material properties are measured according to standard IEEE and DOD definitions and measuring techniques.

PROPERTY SYMBOL UNIT PMN-PT28 PMN-PT30NO OF DAYS AFTER POLING 1 1

ELECTRICAL - LOW FIELDRelative Permittivity 4500-5500 5500-7000Coercive Field EC kV/cm 3.0-3.3 2.5-2.8

ELECTRO-MECHANICALCoupling Factors k33 0.88-0.90 0.90-0.94

kt >0.55 >0.55Charge Constants d33 x 10-12 C/N 1100-1700 1700-2200or Strain Constants d31 x 10-12 C/N or m/V -850 -950Voltage Constants g33 x 10-3 Vm/N >30 >40or Stress Constants g31 x 10-3 Vm/N >17 >15Frequency Constants Nt Hz.m 0800-1900 1800-1900

MECHANICALCompliances SD33 x 10-12 m2/N 10-14 10-14

YE33 x 1010 N/m2 25-30 16-21Poisson’s Ratio σDensity ρ kg/m3 > 8.0 > 8.0

THERMAL DATACurie Temperature Tc °C 143 155Trt Transition Temperature Trt °C 95 ± 5 85 ± 5Approx. Operating Temp. °C 90 80Acoustic Impedance ZA 106 kg/m2sec 28 28

Typical Values measured at 20°C ±1°C are provided for design information only. Standard tolerances areapproximately ±20% of these values. Material properties are measured according to standard IEEE and DODdefinitions and measuring techniques.

PREVIOUS CURRENT MATERIALMATERIAL REFERENCE

NAVY I PC4D PZT401PZT4 PZT402PZT4D PZT403PZT4D PZT404PZT4E PZT405PXE42 PZT406

NAVY II PC5 PZT5A1PZT5A PZT5A2PZT5A PZT5A3PXE59 PZT5A4

NAVY III PZT8 PZT801PZT8 PZT802PZT8L PZT803PZT8S PZT804PXE43 PZT805PC4 PZT806PC8 PZT807

NAVY V PZT5J PZT5J1

NAVY VI PC5H PZT5H1PZT5H PZT5H2

CUSTOM PZT5B PZT501PZT5R PZT502PXE5 PZT503PXE21 PZT504PXE50+ PZT505PXE55 PZT506PXE52 PZT507PZT5T PZT508PC5K PZT5K1n/a PZT5K2n/a PZT5K4

PXE41 PZT407PT2 PT1PZT7A PZT701PZT7D PZT702PXE71 PZT703

MATERIAL CROSS REFERENCE TABLE

r 33T

r 33T

r 33T

r 11T

33T

r 33T

Whether you are experienced with piezoelectric materials, or not, use thischecklist to organise your application data and material requirements. Withthis information, Morgan Electro Ceramics can help you select the most cost,quality, and design effective ceramic elements for your application.

APPLICATIONBriefly describe the device, its function and the transducer function within thedevice. If possible include a drawing, schematic or sketch.

MATERIALRefer to the material tables, and select the material(s) with the requiredcharacteristics. If you need assistance selecting the material, note the operatingrequirements of critical properties.

Navy Type I:Navy Type II:Navy Type III:Navy Type V:Navy Type VI:Custom:Single Crystal:

SIZE & SHAPE

Refer to page 22, and review the shapes and formulae. Select the shape orshapes that satisfy the mounting and physical requirements of the application.Calculate the values of the critical properties for the selected materials, shapes,and sizes. Select the combination that satisfies the mechanical and piezoelectricrequirements of the application.

Tube

Rod

Disc

Ring

Plate

Bar

Bimorph

Unimorph

Actuator

Transducer

Special

MECHANICAL CHARACTERISTICSStandard dimensions and tolerances are listed in page 22. Special dimensionsand tolerances must be negotiated. All dimensions are in metric (mm).

Length:Width:Thickness:Outside Diameter (OD):Inside Diameter (ID):Wall Thickness:Flatness:Other:

ELECTRICAL CHARACTERISTICSThese standard electrical measurements can be made on various MorganElectro Ceramics parts. Minimum values and tolerances must be negotiated.

Capacitance [pF@1kHz]:Resonant Frequency [kHz, MHz]:Vibration mode:Loss factor:d33 or d31 [pC/N]:�f = (fa - fr) [kHz, MHz]:

ELECTRODES

Type:

• Silver

• Nickel

• Gold

• Other (describe)

Placement or Configuration:Ends:ID-OD:Stripes:Wraparound:Shear plate:Polarity Markings:

SPECIAL MATERIAL TESTINGThese tests are usually performed on lot control samples only. Note whichtests, if any, should be performed on the test sample for this order.

High field measurement at kV/mm at 50/60Hz (for “hard” PZT only)Capacitance Change % MaximumLoss factor % Maximumd33 pC/N MinimumImpedance Zr @Fr [�]Density [kg/m3]

SPECIAL REQUIREMENTS:Serial Numbers:Other Requirements:

QUANTITYQuantity required for samples:Potential quantity required for production:

CONTACT DETAILS

Company Name

Address

Town/City

Postcode

Individual Name

Position

Tel/Mobile

Fax

Email

Web Address

ATTACHMENTSList attachments such as drawings, sketches, schematics, and special notes andinstructions.

SAMPLES ORDERING DATA CHECKLIST

39

COMPLIANCEWhen you apply stress to any material, it responds by changing its dimensiondue to its elastic properties. The compliance witnessed in piezoelectricceramics is different in an important way: it exhibits different complianceperpendicularly than it does along its parallel poling axis. For linear positioningapplications, the most important compliance tensor elements are those in thedirection of the PZT extension: S33 for strain due to uniaxial stress along thepoling direction, and S11 for strain due to the perpendicular stress. NormallyS33 is 25% greater than S11. As you might guess from the name, soft PZT issomewhat more compliant than hard PZT.

CURIE TEMPERATURE (Tc)Curie temperature refers to the critical temperature at which crystals in thepiezoelectric ceramic lose their spontaneous polarization and hence theirpiezoelectric property. It is defined as the temperature at which the dielectricconstant is maximized when the temperature is increased.

FREQUENCY CONSTANT (N)The velocity of sound that propagates through a piezoelectric ceramic has aspecific value in each vibration mode when the resonance of other vibrationmodes is not in the vicinity. For a piezoelectric ceramic with a certain shape,the relationship of wavelength � of a vibration with propagation length atthe resonant point is given by equation (69). Because the sound velocity isconstant, we obtain the following equations (70) and (71):

MECHANICAL (Qm)This shows the sharpness of mechanical vibration at the resonant frequency.

POISSON’S RATIO ()This is defined as the ratio of the strain of polarization axis direction and thedistortion of right angle direction to the polarization axis.

REMANENT POLARIZATION (Pr)It is the net polarization remaining in a polycrystalline dielectric material afterremoval of an electric field.

YOUNG’S MODULUS (YE)When stress T is applied to an elastic body within the proportional elasticrange, strain S is given by equation 72:

SE is an elasticity constant (compliance), and Young’s modulus is given as theinverse of compliance. For lengthwise vibrations, the Young’s modulus isgiven by equation 73:

DIELECTRIC CONSTANTThe relative dielectric constant is defined as the ratio of the permittivity of thematerial to the permittivity of free space. This is generally measured wellbelow the mechanical resonance. The dielectric constant is derived from thestatic capacitance measurements at 1 kHz using a standard impedance bridge.

GLOSSARY OF TERMS

38

E

E

EE

TECHNICAL PUBLICATIONS

40

For further information on piezoelectric ceramics, Morgan Electro Ceramics has available the followingtechnical papers on our website:

Measurement of piezoelectric coupling in odd ceramic shapes

Two-channel cylindrical PZT ceramic transducer

Piezoelectric ceramic I.F. filters

Solid-state tuned circuits improve I.F. amplifier reliability

A ceramic bandpass transformer and filter element

An introduction to Morgan Electro Ceramics piezoelectric filters

Design of piezoelectric ladder filters

The electro-acoustic sensitivity of cylindrical ceramic tubes

The stepped horn

Speed of sound in seawater as a function of temperature, pressure and salinity

A primer of ferroelectricity and piezoelectric ceramics

Flexure mode piezoelectric transducer

Piezoelectric high voltage generators

Effects of high static stress on the piezoelectric properties of transducer materials

Power capacities of piezoelectric ceramics in sonar type acoustics transducers

On the meaning of “g” and “d” constant as applied to simple piezoelectric modes of vibration

Useful relationships for ceramic bender Bimorphs®

On the meaning of piezoelectric coupling

Power limitations of piezoelectric ceramics in radiating transducers

Important properties of Morgan Electro Ceramics piezoelectric ceramics (PZT400, PZT5A, PZT5H, PZT800 Series)

Behaviour of piezoelectric ceramics under various environmental and operation conditions of radiating sonar transducers

Useful relationships for circular bender Bimorphs®

Properties of specialised ceramics of Morgan Electro Ceramics (PZT700, Series, PZT-6A1, PZT-6A2, PZT-6B)

Procedures for measuring properties of piezoelectric ceramics

The design of piezoelectric sandwich transducers

Some considerations in the use of cylindrical ceramic elements in transducer design

Some design considerations in the use of Bimorphs® as motor transducers

Piezoelectricity

Piezoelectric and dielectric properties of lead Titanate Zirconate ceramics at low temperatures

Thermal expansion and pyroelectricity in lead Titanate Zirconate and barium Titanate

Stress sensitivity of piezoelectric ceramics: Part 1. Sensitivity to compressive stress parallel to the polar axis

Stress sensitivity of piezoelectric ceramics: Part 2. Heat treatment

Stress sensitivity of piezoelectric ceramics: Part 3. Sensitivity to compressive stress perpendicular to the polar axis

Piezoelectric high voltage transformers

General description of piezoelectric transformers

Cantilever mounted PZT-5A Bimorphs®

TP-23

TP-26

TP-42

TP-43

TP-46

TP-47

TP-50

TP-212

TP-214

TP-215

TP-217

TP-218

TP-219

TP-220

TP-221

TP-222

TP-223

TP-224

TP-225

TP-226

TP-228

TP-230

TP-232

TP-234

TP-235

TP-236

TP-237

TP-238

TP-240

TP-241

TP-242-1

TP-242-2

TP-242-3

TP-243

TP-244

TP-245